# Lattice animal polynomials

## Site animals

### v <= 4

- Perimeter polynomials

```
t1 = 2 n(n - 1);
t2 = 6 - 8 n + 4 n^2;
t3t1 = 12 - 14 n + 6*n^2;
t3t2 = 11 - 14 n + 6*n^2;
t3t3 = 16 - 16 n + 6*n^2;
t4t1 = 32 - 26 n + 8 n^2;
t4t2 = 24 - 24 n + 8 n^2;
t4t3 = 26 - 24 n + 8 n^2;
t4t4 = 28 - 24 n + 8 n^2;
t4t5 = 20 - 22 n + 8 n^2;
t4t6 = 21 - 22 n + 8 n^2;
t4t7 = 22 - 22 n + 8 n^2;
t4t8 = 14 - 20 n + 8 n^2;
t4t9 = 15 - 20 n + 8 n^2;
t4t10 = 16 - 20 n + 8 n^2;
t4t11 = 17 - 20 n + 8 n^2;
t4t12 = 18 - 20 n + 8 n^2;
```

- Count polynomials

```
g1 = 1;
g2 = n (n - 1);
g3g1 = n(n - 1)(-7 + 4 n);
g3g2 = 2 n(n - 1) (7 - 5 n + n^2);
g3g3 = 4/3 n(n - 1)(n - 2);
g4g1 = 2/3 n(n - 1)(n - 2)(n - 3);
g4g2 = 1/3 n(n - 1)(n - 2);
g4g3 = 4 n(n - 1)(n - 2)(n - 2);
g4g4 = 1/2 n(n - 1)(n - 2)(n - 3);
g4g5 = 1/2 n(n - 1)(-383 + 416 n - 144 n^2 + 16 n^3);
g4g6 = 8 n(n - 1)(n - 2)(-5 + 2 n);
g4g7 = 4 n(n - 1)(n - 2)(-3 + 2 n);
g4g8 = 8 n(n - 1)(n - 2)(12 - 7 n + n^2);
g4g9 = 4/3 n(n - 1)(n - 2)(n - 3)(23 - 9 n + n^2);
g4g10 = 4 n(n - 1)(7 - 5 n + n^2)^2;
g4g11 = 4 n(n - 1)(-39 + 54 n - 25 n^2 + 4 n^3);
g4g12 = 1/3 n(n - 1)(139 - 164 n + 48 n^2);
```
### v = 5

- Perimeter polynomials

```
t5t1 = 55 - 38 n + 10 n^2;
t5t2 = 48 - 36 n + 10 n^2;
t5t3 = 40 - 34 n + 10 n^2;
t5t4 = 41 - 34 n + 10 n^2;
t5t5 = 42 - 34 n + 10 n^2;
t5t6 = 34 - 32 n + 10 n^2;
t5t7 = 35 - 32 n + 10 n^2;
t5t8 = 36 - 32 n + 10 n^2;
t5t9 = 37 - 32 n + 10 n^2;
t5t10 = 38 - 32 n + 10 n^2;
t5t11 = 27 - 30 n + 10 n^2;
t5t12 = 28 - 30 n + 10 n^2;
t5t13 = 29 - 30 n + 10 n^2;
t5t14 = 30 - 30 n + 10 n^2;
t5t15 = 31 - 30 n + 10 n^2;
t5t16 = 32 - 30 n + 10 n^2;
t5t17 = 33 - 30 n + 10 n^2;
t5t18 = 34 - 30 n + 10 n^2;
t5t19 = 21 - 28 n + 10 n^2;
t5t20 = 22 - 28 n + 10 n^2;
t5t21 = 23 - 28 n + 10 n^2;
t5t22 = 24 - 28 n + 10 n^2;
t5t23 = 25 - 28 n + 10 n^2;
t5t24 = 26 - 28 n + 10 n^2;
t5t25 = 27 - 28 n + 10 n^2;
t5t26 = 28 - 28 n + 10 n^2;
t5t27 = 15 - 26 n + 10 n^2;
t5t28 = 16 - 26 n + 10 n^2;
t5t29 = 17 - 26 n + 10 n^2;
t5t30 = 18 - 26 n + 10 n^2;
t5t31 = 19 - 26 n + 10 n^2;
t5t32 = 20 - 26 n + 10 n^2;
t5t33 = 21 - 26 n + 10 n^2;
t5t34 = 22 - 26 n + 10 n^2;
t5t35 = 23 - 26 n + 10 n^2;
t5t36 = 24 - 26 n + 10 n^2;
```
- Count polynomials

```
g5g1 = 4/15 n (n - 1) (-24 + 26 n - 9 n^2 + n^3);
g5g2 = 4/3 n (n - 1) (6 - 5 n + n^2);
g5g3 = 8/3 n (n - 1) (6 - 5 n + n^2);
g5g4 = n (n - 1) (10 - 9 n + 2 n^2);
g5g5 = 8 n (n - 1) (-18 + 21 n - 8 n^2 + n^3);
g5g6 = 4 n (n - 1) (-2 + n);
g5g7 = 8/3 n (n - 1) (96 - 152 n + 88 n^2 - 22 n^3 + 2 n^4);
g5g8 = 4 n (n - 1) (-36 + 52 n - 25 n^2 + 4 n^3);
g5g9 = 8 n (n - 1) (-12 + 16 n - 7 n^2 + n^3);
g5g10 = 8/3 n (n - 1) (-12 + 22 n - 12 n^2 + 2 n^3);
g5g11 = 8/3 n (n - 1) (-24 + 26 n - 9 n^2 + n^3);
g5g12 = 8 n (n - 1) (120 - 154 n + 71 n^2 - 14 n^3 + n^4);
g5g13 = 8 n (n - 1) (102 - 157 n + 89 n^2 - 22 n^3 + 2 n^4);
g5g14 = 2 n (n - 1) (74 - 257 n + 222 n^2 - 72 n^3 + 8 n^4);
g5g15 = 8/5 n (n - 1) (-488 + 642 n - 283 n^2 + 42 n^3);
g5g16 = 2 n (n - 1) (274 - 289 n + 104 n^2 - 18 n^3 + 2 n^4);
g5g17 = 4 n (n - 1) (n - 2) (45 - 27 n + 4 n^2);
g5g18 = 8 n (n - 1) (n - 2) (-3 + n);
g5g19 = 8 n (n - 1) (n - 2) (-120 + 94 n - 24 n^2 + 2 n^3);
g5g20 = 8 n (n - 1) (n - 2) (-240 + 188 n - 48 n^2 + 4 n^3);
g5g21 = 8 n (n - 1) (-480 + 688 n - 386 n^2 + 109 n^3 - 16 n^4 + n^5);
g5g22 = 4 n (n - 1) (-1218 + 1897 n - 1178 n^2 + 371 n^3 - 60 n^4 + 4 n^5);
g5g23 = 4 n (n - 1) (-539 + 882 n - 618 n^2 + 236 n^3 - 48 n^4 + 4 n^5);
g5g24 = 4 n (n - 1) (926 - 1485 n + 891 n^2 - 238 n^3 + 24 n^4);
g5g25 = 4 n (n - 1) (n - 2) (64 - 65 n + 6 n^2 + 4 n^3);
g5g26 = 8 n (n - 1) (n - 2) (15 - 19 n + 6 n^2);
g5g27 = 8 n (n - 1) (n - 2) (-240 + 188 n - 48 n^2 + 4 n^3);
g5g28 = 4 n (n - 1) (n - 2) (-708 + 569 n - 150 n^2 + 13 n^3);
g5g29 = 24 n (n - 1) (-72 + 78 n - 27 n^2 + 3 n^3);
g5g30 = 2/3 n (n - 1) (-24678 + 35565 n - 19535 n^2 + 5091 n^3 - 611 n^4 + 21 n^5 + n^6);
g5g31 = 2 n (n - 1) (-4110 + 7043 n - 4822 n^2 + 1658 n^3 - 287 n^4 + 20 n^5);
g5g32 = 1/2 n (n - 1) (59527 - 96213 n + 62105 n^2 - 20616 n^3 + 3760 n^4 - 368 n^5 + 16 n^6);
g5g33 = 2/3 n (n - 1) (-20301 + 28217 n - 13623 n^2 + 2140 n^3 + 294 n^4 - 132 n^5 + 12 n^6);
g5g34 = n (n - 1) (1492 + 461 n - 2648 n^2 + 1800 n^3 - 484 n^4 + 48 n^5);
g5g35 = 2 n (n - 1) (377 - 1073 n + 963 n^2 - 356 n^3 + 48 n^4);
g5g36 = n (n - 1) (-279 + 524 n - 320 n^2 + 64 n^3);
```
### v = 6

- Perimeter polynomials

```
t6t1 = 86 - 52 n + 12 n^2;
t6t2 = 78 - 50 n + 12 n^2;
t6t3 = 70 - 48 n + 12 n^2;
t6t4 = 62 - 46 n + 12 n^2;
t6t5 = 63 - 46 n + 12 n^2;
t6t6 = 65 - 46 n + 12 n^2;
t6t7 = 54 - 44 n + 12 n^2;
t6t8 = 56 - 44 n + 12 n^2;
t6t9 = 57 - 44 n + 12 n^2;
t6t10 = 58 - 44 n + 12 n^2;
t6t11 = 59 - 44 n + 12 n^2;
t6t12 = 60 - 44 n + 12 n^2;
t6t13 = 61 - 44 n + 12 n^2;
t6t14 = 49 - 42 n + 12 n^2;
t6t15 = 50 - 42 n + 12 n^2;
t6t16 = 51 - 42 n + 12 n^2;
t6t17 = 52 - 42 n + 12 n^2;
t6t18 = 53 - 42 n + 12 n^2;
t6t19 = 54 - 42 n + 12 n^2;
t6t20 = 42 - 40 n + 12 n^2;
t6t21 = 43 - 40 n + 12 n^2;
t6t22 = 44 - 40 n + 12 n^2;
t6t23 = 45 - 40 n + 12 n^2;
t6t24 = 46 - 40 n + 12 n^2;
t6t25 = 47 - 40 n + 12 n^2;
t6t26 = 48 - 40 n + 12 n^2;
t6t27 = 50 - 40 n + 12 n^2;
t6t28 = 34 - 38 n + 12 n^2;
t6t29 = 36 - 38 n + 12 n^2;
t6t30 = 37 - 38 n + 12 n^2;
t6t31 = 38 - 38 n + 12 n^2;
t6t32 = 39 - 38 n + 12 n^2;
t6t33 = 40 - 38 n + 12 n^2;
t6t34 = 41 - 38 n + 12 n^2;
t6t35 = 42 - 38 n + 12 n^2;
t6t36 = 43 - 38 n + 12 n^2;
t6t37 = 44 - 38 n + 12 n^2;
t6t38 = 26 - 36 n + 12 n^2;
t6t39 = 28 - 36 n + 12 n^2;
t6t40 = 29 - 36 n + 12 n^2;
t6t41 = 30 - 36 n + 12 n^2;
t6t42 = 31 - 36 n + 12 n^2;
t6t43 = 32 - 36 n + 12 n^2;
t6t44 = 33 - 36 n + 12 n^2;
t6t45 = 34 - 36 n + 12 n^2;
t6t46 = 35 - 36 n + 12 n^2;
t6t47 = 36 - 36 n + 12 n^2;
t6t48 = 37 - 36 n + 12 n^2;
t6t49 = 38 - 36 n + 12 n^2;
t6t50 = 39 - 36 n + 12 n^2;
t6t51 = 40 - 36 n + 12 n^2;
t6t52 = 20 - 34 n + 12 n^2;
t6t53 = 21 - 34 n + 12 n^2;
t6t54 = 22 - 34 n + 12 n^2;
t6t55 = 23 - 34 n + 12 n^2;
t6t56 = 24 - 34 n + 12 n^2;
t6t57 = 25 - 34 n + 12 n^2;
t6t58 = 26 - 34 n + 12 n^2;
t6t59 = 27 - 34 n + 12 n^2;
t6t60 = 28 - 34 n + 12 n^2;
t6t61 = 29 - 34 n + 12 n^2;
t6t62 = 30 - 34 n + 12 n^2;
t6t63 = 31 - 34 n + 12 n^2;
t6t64 = 32 - 34 n + 12 n^2;
t6t65 = 33 - 34 n + 12 n^2;
t6t66 = 34 - 34 n + 12 n^2;
t6t67 = 14 - 32 n + 12 n^2;
t6t68 = 15 - 32 n + 12 n^2;
t6t69 = 16 - 32 n + 12 n^2;
t6t70 = 17 - 32 n + 12 n^2;
t6t71 = 18 - 32 n + 12 n^2;
t6t72 = 19 - 32 n + 12 n^2;
t6t73 = 20 - 32 n + 12 n^2;
t6t74 = 21 - 32 n + 12 n^2;
t6t75 = 22 - 32 n + 12 n^2;
t6t76 = 23 - 32 n + 12 n^2;
t6t77 = 24 - 32 n + 12 n^2;
t6t78 = 25 - 32 n + 12 n^2;
t6t79 = 26 - 32 n + 12 n^2;
t6t80 = 27 - 32 n + 12 n^2;
t6t81 = 28 - 32 n + 12 n^2;
t6t82 = 29 - 32 n + 12 n^2;
t6t83 = 30 - 32 n + 12 n^2;
```
- Count polynomials

```
g6g1 = 8/90 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5);
g6g2 = 2/3 n (n - 1) (n - 2) (n - 3) (n - 4);
g6g3 = n (n - 1) (n - 2) (n - 3);
g6g4 = 1/6 n (n - 1) (n - 2);
g6g5 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4);
g6g6 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-7 + 2 n);
g6g7 = 1/3 n (n - 1) (n - 2) (n - 3) (7);
g6g8 = 8/3 n (n - 1) (n - 2) (n - 3) (-7 + 3 n);
g6g9 = 8/3 n (n - 1) (n - 2) (n - 3) (-141 + 80 n - 15 n^2 + n^3);
g6g10 = 2/3 n (n - 1) (n - 2) (n - 3) (281 - 150 n + 22 n^2);
g6g11 = 8 n (n - 1) (n - 2) (n - 3) (n - 4);
g6g12 = 20/3 n (n - 1) (n - 2) (n - 3) (n - 4);
g6g13 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-3 + n);
g6g14 = 4 n (n - 1) (n - 2) (49 - 28 n + 4 n^2);
g6g15 = 8/5 n (n - 1) (n - 2) (n - 3) (477 - 213 n + 25 n^2);
g6g16 = 4/3 n (n - 1) (n - 2) (-759 + 749 n - 249 n^2 + 28 n^3);
g6g17 = 4 n (n - 1) (n - 2) (n - 3) (-35 - 2 n + 4 n^2);
g6g18 = 8 n (n - 1) (n - 2) (n - 3) (-4 + 2 n);
g6g19 = 20/3 n (n - 1) (n - 2) (n - 3) (-5 + 2 n);
g6g20 = 1/3 n (n - 1) (n - 2) (8643 - 8688 n + 3232 n^2 - 528 n^3 + 32 n^4);
g6g21 = 2/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-627 + 134 n);
g6g22 = 4 n (n - 1) (n - 2) (1488 - 1517 n + 599 n^2 - 110 n^3 + 8 n^4);
g6g23 = 4/3 n (n - 1) (n - 2) (1575 - 2054 n + 1062 n^2 - 256 n^3 + 24 n^4);
g6g24 = 1/3 n (n - 1) (n - 2) (-7061 + 4919 n - 692 n^2 - 192 n^3 + 48 n^4);
g6g25 = 2 n (n - 1) (n - 2) (221 + 143 n - 168 n^2 + 32 n^3);
g6g26 = 2/3 n (n - 1) (n - 2) (n - 3) (361 - 351 n + 83 n^2);
g6g27 = n (n - 1) (-90 + 99 n - 35 n^2 + 4 n^3);
g6g28 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (-22 + 4 n);
g6g29 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (164 - 72 n + 8 n^2);
g6g30 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-658 + 204 n - 24 n^2 + 2 n^3);
g6g31 = 8/3 n (n - 1) (n - 2) (n - 3) (-391 + 20 n + 148 n^2 - 56 n^3 + 6 n^4);
g6g32 = 4 n (n - 1) (n - 2) (3779 - 4720 n + 2258 n^2 - 488 n^3 + 40 n^4);
g6g33 = 2/3 n (n - 1) (n - 2) (-32535 + 35438 n - 14158 n^2 + 2628 n^3 - 260 n^4 + 16 n^5);
g6g34 = 8/3 n (n - 1) (n - 2) (9477 - 9551 n + 3643 n^2 - 652 n^3 + 50 n^4);
g6g35 = 2 n (n - 1) (n - 2) (-7817 + 6910 n - 2124 n^2 + 232 n^3);
g6g36 = 8/3 n (n - 1) (n - 2) (n - 3) (-596 + 226 n - 24 n^2 + 4 n^3);
g6g37 = 4/3 n (n - 1) (n - 2) (n - 3) (193 - 116 n + 28 n^2);
g6g38 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (n - 6);
g6g39 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (-38 + 8 n);
g6g40 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-209 + 37 n + n^2);
g6g41 = 4/3 n (n - 1) (n - 2) (n - 3) (n - 4) (1055 - 410 n - 18 n^2 + 12 n^3);
g6g42 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (359 - 178 n - 6 n^2 + 6 n^3);
g6g43 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-1926 + 1281 n - 316 n^2 + 30 n^3);
g6g44 = 8/3 n (n - 1) (n - 2) (n - 3) (4636 - 4577 n + 1840 n^2 - 366 n^3 + 30 n^4);
g6g45 = n (n - 1) (-51263 + 69816 n - 31124 n^2 + 2116 n^3 + 2384 n^4 - 720 n^5 + 64 n^6);
g6g46 = 4 n (n - 1) (n - 2) (3453 - 4107 n + 1827 n^2 - 262 n^3 - 33 n^4 + 9 n^5);
g6g47 = 4 n (n - 1) (n - 2) (-3240 + 2387 n - 289 n^2 - 118 n^3 + 15 n^4 + 3 n^5);
g6g48 = 2/3 n (n - 1) (n - 2) (6394 - 1839 n - 1428 n^2 + 552 n^3 - 60 n^4 + 12 n^5);
g6g49 = 2 n (n - 1) (n - 2) (-1324 + 277 n + 320 n^2 - 154 n^3 + 24 n^4);
g6g50 = 8 n (n - 1) (n - 2) (n - 3) (-23 - 30 n + 10 n^2);
g6g51 = 8 n (n - 1) (n - 2) (n - 3) (-1 + 4 n);
g6g52 = 64 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (n - 6);
g6g53 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (-93 + 16 n);
g6g54 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (1263 - 532 n + 56 n^2);
g6g55 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (2116 - 1022 n + 120 n^2);
g6g56 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (610 - 180 n - 8 n^2 + 4 n^3);
g6g57 = 8/3 n (n - 1) (n - 2) (n - 3) (n - 4) (-9318 + 4294 n - 692 n^2 + 32 n^3 + 2 n^4);
g6g58 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (-3336 + 2099 n - 459 n^2 + 36 n^3);
g6g59 = 4 n (n - 1) (n - 2) (n - 3) (-19291 + 15931 n - 5345 n^2 + 1010 n^3 - 124 n^4 + 8 n^5);
g6g60 = 4/3 n (n - 1) (n - 2) (n - 3) (-56889 + 52634 n - 19881 n^2 + 4076 n^3 - 504 n^4 + 32 n^5);
g6g61 = 2 n (n - 1) (-109511 + 262476 n - 260556 n^2 + 139396 n^3 - 43740 n^4 + 8160 n^5 - 856 n^6 + 40 n^7);
g6g62 = 2 n (n - 1) (208783 - 373900 n + 271620 n^2 - 101656 n^3 + 19884 n^4 - 1540 n^5 - 80 n^6 + 16 n^7);
g6g63 = 2/3 n (n - 1) (-160100 + 148873 n + 16662 n^2 - 68272 n^3 + 32384 n^4 - 6516 n^5 + 504 n^6);
g6g64 = 4 n (n - 1) (n - 2) (1127 - 6604 n + 5549 n^2 - 1666 n^3 + 148 n^4 + 8 n^5);
g6g65 = 8 n (n - 1) (n - 2) (-213 + 341 n - 48 n^2 - 80 n^3 + 24 n^4);
g6g66 = 8/3 n (n - 1) (n - 2) (-381 + 753 n - 480 n^2 + 100 n^3);
g6g67 = 64 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (n - 6);
g6g68 = 48 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (-22 + 4 n);
g6g69 = 2 n (n - 1) (n - 2) (n - 3) (n - 4) (4995 - 1998 n + 200 n^2);
g6g70 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (530 - 274 n + 34 n^2);
g6g71 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (1064 - 482 n + 54 n^2);
g6g72 = 8 n (n - 1) (n - 2) (n - 3) (n - 4) (-4882 + 2436 n - 430 n^2 + 28 n^3);
g6g73 = 4/15 n (n - 1) (n - 2) (n - 3) (n - 4) (-146535 + 96734 n - 22705 n^2 + 2025 n^3 - 35 n^4 + n^5);
g6g74 = 4/3 n (n - 1) (n - 2) (n - 3) (-94383 + 77906 n - 25201 n^2 + 4326 n^3 - 467 n^4 + 28 n^5);
g6g75 = n (n - 1) (n - 2) (n - 3) (65103 - 33925 n + 1985 n^2 + 1760 n^3 - 416 n^4 + 32 n^5);
g6g76 = 4/3 n (n - 1) (n - 2) (n - 3) (-261506 + 254905 n - 100926 n^2 + 19942 n^3 - 1846 n^4 + 36 n^5 + 4 n^6);
g6g77 = 2/3 n (n - 1) (n - 2) (n - 3) (170522 - 144767 n + 35983 n^2 + 90 n^3 - 1046 n^4 + 70 n^5 + 6 n^6);
g6g78 = 4/5 n (n - 1) (n - 2) (n - 3) (288279 - 400536 n + 228115 n^2 - 67810 n^3 + 11115 n^4 - 980 n^5 + 40 n^6);
g6g79 = 1/3 n (n - 1) (-3047598 + 6860093 n - 6326650 n^2 + 3086922 n^3 - 851249 n^4 + 127480 n^5 - 7752 n^6 - 288 n^7 + 48 n^8);
g6g80 = 4/3 n (n - 1) (232335 - 513070 n + 427948 n^2 - 164369 n^3 + 24080 n^4 + 2142 n^5 - 1080 n^6 + 96 n^7);
g6g81 = 2 n (n - 1) (-22175 + 37793 n - 14369 n^2 - 7578 n^3 + 7276 n^4 - 2000 n^5 + 192 n^6);
g6g82 = 8 n (n - 1) (-43 + 1338 n - 2478 n^2 + 1742 n^3 - 544 n^4 + 64 n^5);
g6g83 = n (n - 1) (1497 - 4068 n + 3964 n^2 - 1664 n^3 + 256 n^4);
```

## Bond animals

### e <= 3

- Perimeter polynomials

```
t1 = 4 n(n - 1) - 2;
t2t1 = -5 - 6 n + 6 n^2;
t2t2 = -4 - 6 n + 6 n^2;
t3t1 = -6 - 6 n + 6 n^2;
t3t2 = -9 - 8 n + 8 n^2;
t3t3 = -8 - 8 n + 8 n^2;
t3t4 = -7 - 8 n + 8 n^2;
t3t5 = -6 - 8 n + 8 n^2;
```
- Count polynomials

```
g1 = n(n - 1);
g2g1 = 2 n (n - 1) (-4 + 2 n);
g2g2 = n (n - 1) (7 - 6 n + 2 n^2);
g3g1 = 2/3 n (n - 1) (-4 + 2 n);
g3g2 = 16/3 n (n - 1) (10 - 9 n + 2 n^2);
g3g3 = 32 n (n - 1) (4 - 4 n + n^2);
g3g4 = 2 n (n - 1) (-125 + 157 n - 71 n^2 + 12 n^3);
g3g5 = 1/3 n (n - 1) (235 - 408 n + 296 n^2 - 104 n^3 + 16 n^4);
```

### e = 4

- Perimeter polynomials

```
t4t1 = -10 - 8 n + 8 n^2;
t4t2 = -9 - 8 n + 8 n^2;
t4t3 = -8 - 8 n + 8 n^2;
t4t4 = -14 - 10 n + 10 n^2;
t4t5 = -13 - 10 n + 10 n^2;
t4t6 = -12 - 10 n + 10 n^2;
t4t7 = -11 - 10 n + 10 n^2;
t4t8 = -10 - 10 n + 10 n^2;
t4t9 = -9 - 10 n + 10 n^2;
t4t10 = -8 - 10 n + 10 n^2;
```
- Count polynomials

```
g4g1 = 5 n (n - 1) (10 - 9 n + 2 n^2);
g4g2 = 20 n (n - 1) (n - 2)^2;
g4g3 = 1/2 n (n - 1) (-169 + 211 n - 95 n^2 + 16 n^3);
g4g4 = 100/3 n (n - 1) (n - 2) (n - 3) (n - 4);
g4g5 = 300 n (n - 1) (n - 2) (n - 3);
g4g6 = n (n - 1) (n - 2) (2815 - 1830 n + 320 n^2);
g4g7 = 4/3 n (n - 1) (n - 2) (-345 + 302 n - 228 n^2 + 64 n^3);
g4g8 = 4 n (n - 1) (n - 2) (-1041 + 1254 n - 529 n^2 + 82 n^3);
g4g9 = 4 n (n - 1) (-1540 + 3208 n - 2776 n^2 + 1251 n^3 - 296 n^4 + 30 n^5);
g4g10 = 1/6 n (n - 1) (8187 - 18937 n + 20239 n^2 - 12596 n^3 + 4744 n^4 - 1020 n^5 + 100 n^6);
```

### e = 5

- Perimeter polynomials

```
t5t1 = -11 - 8 n + 8 n^2;
t5t2 = -10 - 8 n + 8 n^2;
t5t3 = -15 - 10 n + 10 n^2;
t5t4 = -14 - 10 n + 10 n^2;
t5t5 = -13 - 10 n + 10 n^2;
t5t6 = -12 - 10 n + 10 n^2;
t5t7 = -11 - 10 n + 10 n^2;
t5t8 = -10 - 10 n + 10 n^2;
t5t9 = -20 - 12 n + 12 n^2;
t5t10 = -19 - 12 n + 12 n^2;
t5t11 = -18 - 12 n + 12 n^2;
t5t12 = -17 - 12 n + 12 n^2;
t5t13 = -16 - 12 n + 12 n^2;
t5t14 = -15 - 12 n + 12 n^2;
t5t15 = -14 - 12 n + 12 n^2;
t5t16 = -13 - 12 n + 12 n^2;
t5t17 = -12 - 12 n + 12 n^2;
t5t18 = -11 - 12 n + 12 n^2;
t5t19 = -10 - 12 n + 12 n^2;
```

- Count polynomials

```
g5g1 = 2 n (n - 1) (n - 2) (-5 + 2 n);
g5g2 = 4 n (n - 1) (n - 2) (-2 + n);
g5g3 = 296/5 n (n - 1) (n - 2) (n - 3) (n - 4);
g5g4 = 12 n (n - 1) (n - 2) (n - 3) (37);
g5g5 = 4 n (n - 1) (n - 2) (847 - 550 n + 96 n^2);
g5g6 = 8 n (n - 1) (n - 2) (-60 + 53 n - 37 n^2 + 10 n^3);
g5g7 = 4 n (n - 1) (n - 2) (-683 + 810 n - 338 n^2 + 52 n^3);
g5g8 = 4/5 n (n - 1) (-2601 + 5409 n - 4671 n^2 + 2099 n^3 - 495 n^4 + 50 n^5);
g5g9 = 576/5 n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5);
g5g10 = 576 n (n - 1) (n - 2) (n - 3) (n - 4);
g5g11 = 288 n (n - 1) (n - 2) (n - 3) (-14 + 5 n);
g5g12 = 16 n (n - 1) (n - 2) (-3041 + 2761 n - 882 n^2 + 100 n^3);
g5g13 = 4/3 n (n - 1) (n - 2) (82905 - 66366 n + 18768 n^2 - 2674 n^3 + 250 n^4);
g5g14 = 4/5 n (n - 1) (n - 2) (-352532 + 336077 n - 111066 n^2 + 12870 n^3);
g5g15 = 2 n (n - 1) (n - 2) (130073 - 153724 n + 74843 n^2 - 18142 n^3 + 1856 n^4);
g5g16 = 4/3 n (n - 1) (n - 2) (27447 - 67566 n + 42948 n^2 - 8060 n^3 - 1000 n^4 + 384 n^5);
g5g17 = n (n - 1) (343289 - 853627 n + 898259 n^2 - 513828 n^3 + 169230 n^4 - 30616 n^5 + 2400 n^6);
g5g18 = 4 n (n - 1) (-45090 + 118021 n - 141749 n^2 + 100302 n^3 - 44631 n^4 + 12400 n^5 - 1992 n^6 + 144 n^7);
g5g19 = 1/5 (-1 + n) n (97331 - 353612 n + 535858 n^2 - 469102 n^3 + 267852 n^4 - 103312 n^5 + 26288 n^6 - 4032 n^7 + 288 n^8);
```