Number of k-polyominoes for small parameters
A k-polyomino is a non-overlapping union of n regular unit k-gons.
| k/n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
| 3 |
1 |
1 |
1 |
3 |
4 |
12 |
24 |
66 |
160 |
448 |
1186 |
| 4 |
1 |
1 |
2 |
5 |
12 |
35 |
108 |
369 |
1285 |
4655 |
17073 |
| 5 |
1 |
1 |
2 |
7 |
25 |
118 |
551 |
2812 |
14445 |
76092 |
403976 |
| 6 |
1 |
1 |
3 |
7 |
22 |
82 |
333 |
1448 |
6572 |
30490 |
143552 |
| 7 |
1 |
1 |
2 |
7 |
25 |
118 |
558 |
2876 |
14982 |
80075 |
431889 |
| 8 |
1 |
1 |
3 |
11 |
50 |
269 |
1605 |
10102 |
65323 |
430302 |
|
| 9 |
1 |
1 |
3 |
14 |
82 |
585 |
4418 |
34838 |
280014 |
|
|
| 10 |
1 |
1 |
4 |
19 |
127 |
985 |
8350 |
73675 |
|
|
|
| 11 |
1 |
1 |
4 |
23 |
186 |
1750 |
17507 |
181127 |
|
|
|
| 12 |
1 |
1 |
5 |
23 |
168 |
1438 |
13512 |
131801 |
|
|
|
| 13 |
1 |
1 |
4 |
23 |
187 |
1765 |
17775 |
185297 |
|
|
|
| 14 |
1 |
1 |
5 |
29 |
263 |
2718 |
30467 |
352375 |
|
|
|
| 15 |
1 |
1 |
5 |
35 |
362 |
4336 |
55264 |
|
|
|
|
| 16 |
1 |
1 |
6 |
42 |
472 |
6040 |
83252 |
|
|
|
|
| 17 |
1 |
1 |
6 |
48 |
614 |
8814 |
134422 |
|
|
|
|
| 18 |
1 |
1 |
7 |
47 |
566 |
7678 |
112514 |
|
|
|
|
| 19 |
1 |
1 |
6 |
48 |
615 |
8839 |
135175 |
|
|
|
|
| 20 |
1 |
1 |
7 |
57 |
776 |
11876 |
195122 |
|
|
|
|
| 21 |
1 |
1 |
7 |
64 |
972 |
16410 |
294091 |
|
|
|
|
| 22 |
1 |
1 |
8 |
74 |
1179 |
20970 |
397852 |
|
|
|
|
| 23 |
1 |
1 |
8 |
82 |
1437 |
27720 |
566007 |
|
|
|
|
| 24 |
1 |
1 |
9 |
81 |
1347 |
24998 |
|
|
|
|
|
| 25 |
1 |
1 |
8 |
82 |
1439 |
27787 |
|
|
|
|
|
| 26 |
1 |
1 |
9 |
93 |
1711 |
34763 |
|
|
|
|
|
| 27 |
1 |
1 |
9 |
103 |
2045 |
44687 |
|
|
|
|
|
| 28 |
1 |
1 |
10 |
115 |
2376 |
54133 |
|
|
|
|
|
| 29 |
1 |
1 |
10 |
125 |
2786 |
67601 |
|
|
|
|
|
| 30 |
1 |
1 |
11 |
123 |
2641 |
62252 |
|
|
|
|
|
| 31 |
1 |
1 |
10 |
125 |
2790 |
67777 |
|
|
|
|
|
| 32 |
1 |
1 |
11 |
139 |
3204 |
81066 |
|
|
|
|
|
| 33 |
1 |
1 |
11 |
150 |
3707 |
99420 |
|
|
|
|
|
| 34 |
1 |
1 |
12 |
165 |
4193 |
116465 |
|
|
|
|
|
| 35 |
1 |
1 |
12 |
177 |
4790 |
140075 |
|
|
|
|
|
| 36 |
1 |
1 |
13 |
175 |
4575 |
130711 |
|
|
|
|
|
| 37 |
1 |
1 |
12 |
177 |
4796 |
140434 |
|
|
|
|
|
| 38 |
1 |
1 |
13 |
193 |
5380 |
163027 |
|
|
|
|
|
| 39 |
1 |
1 |
13 |
207 |
6089 |
193587 |
|
|
|
|
|
| 40 |
1 |
1 |
14 |
224 |
6760 |
221521 |
|
|
|
|
|
| 41 |
1 |
1 |
14 |
238 |
7578 |
259396 |
|
|
|
|
|
| 42 |
1 |
1 |
15 |
235 |
7282 |
244564 |
|
|
|
|
|
| 43 |
1 |
1 |
14 |
238 |
7584 |
259838 |
|
|
|
|
|
| 44 |
1 |
1 |
15 |
257 |
8373 |
295558 |
|
|
|
|
|
| 45 |
1 |
1 |
15 |
272 |
9321 |
342841 |
|
|
|
|
|
| 46 |
1 |
1 |
16 |
292 |
10207 |
385546 |
|
|
|
|
|
| 47 |
1 |
1 |
16 |
308 |
11282 |
442543 |
|
|
|
|
|
| 48 |
1 |
1 |
17 |
305 |
10890 |
420154 |
|
|
|
|
|
| 49 |
1 |
1 |
16 |
308 |
11290 |
443178 |
|
|
|
|
|
| 50 |
1 |
1 |
17 |
329 |
12309 |
495988 |
|
|
|
|
|
| 51 |
1 |
1 |
17 |
347 |
13532 |
565225 |
|
|
|
|
|
| 52 |
1 |
1 |
18 |
369 |
14663 |
627172 |
|
|
|
|
|
| 53 |
1 |
1 |
18 |
387 |
16029 |
|
|
|
|
|
|
| 54 |
1 |
1 |
19 |
383 |
15527 |
|
|
|
|
|
|
| 55 |
1 |
1 |
18 |
387 |
16037 |
|
|
|
|
|
|
| 56 |
1 |
1 |
19 |
411 |
17321 |
|
|
|
|
|
|
| 57 |
1 |
1 |
19 |
430 |
18849 |
|
|
|
|
|
|
| 58 |
1 |
1 |
20 |
455 |
20257 |
|
|
|
|
|
|
| 59 |
1 |
1 |
20 |
475 |
21948 |
|
|
|
|
|
|
| 60 |
1 |
1 |
21 |
471 |
21327 |
|
|
|
|
|
|
| 61 |
1 |
1 |
20 |
475 |
21959 |
|
|
|
|
|
|
| 62 |
1 |
1 |
21 |
501 |
23534 |
|
|
|
|
|
|
| 63 |
1 |
1 |
21 |
523 |
25411 |
|
|
|
|
|
|
| 64 |
1 |
1 |
22 |
550 |
27117 |
|
|
|
|
|
|
| 65 |
1 |
1 |
22 |
572 |
|
|
|
|
|
|
|
| 66 |
1 |
1 |
23 |
567 |
|
|
|
|
|
|
|
| 67 |
1 |
1 |
22 |
572 |
|
|
|
|
|
|
|
| 68 |
1 |
1 |
23 |
601 |
|
|
|
|
|
|
|
| 69 |
1 |
1 |
23 |
624 |
|
|
|
|
|
|
|
| 70 |
1 |
1 |
24 |
654 |
|
|
|
|
|
|
|
| 71 |
1 |
1 |
24 |
678 |
|
|
|
|
|
|
|
| 72 |
1 |
1 |
25 |
673 |
|
|
|
|
|
|
|
| 73 |
1 |
1 |
24 |
678 |
|
|
|
|
|
|
|
| 74 |
1 |
1 |
25 |
709 |
|
|
|
|
|
|
|
| 75 |
1 |
1 |
25 |
735 |
|
|
|
|
|
|
|
| 76 |
1 |
1 |
26 |
767 |
|
|
|
|
|
|
|
| 77 |
1 |
1 |
26 |
793 |
|
|
|
|
|
|
|
| 78 |
1 |
1 |
27 |
787 |
|
|
|
|
|
|
|
| 79 |
1 |
1 |
26 |
793 |
|
|
|
|
|
|
|
| 80 |
1 |
1 |
27 |
827 |
|
|
|
|
|
|
|
| 81 |
1 |
1 |
27 |
854 |
|
|
|
|
|
|
|
| 82 |
1 |
1 |
28 |
889 |
|
|
|
|
|
|
|
| 83 |
1 |
1 |
28 |
917 |
|
|
|
|
|
|
|
| 84 |
1 |
1 |
29 |
911 |
|
|
|
|
|
|
|
| 85 |
1 |
1 |
28 |
917 |
|
|
|
|
|
|
|
| 86 |
1 |
1 |
29 |
953 |
|
|
|
|
|
|
|
| 87 |
1 |
1 |
29 |
983 |
|
|
|
|
|
|
|
| 88 |
1 |
1 |
30 |
1020 |
|
|
|
|
|
|
|
| 89 |
1 |
1 |
30 |
1050 |
|
|
|
|
|
|
|
| 90 |
1 |
1 |
31 |
1043 |
|
|
|
|
|
|
|
| 91 |
1 |
1 |
30 |
1050 |
|
|
|
|
|
|
|
| 92 |
1 |
1 |
31 |
1089 |
|
|
|
|
|
|
|
| 93 |
1 |
1 |
31 |
1120 |
|
|
|
|
|
|
|
| 94 |
1 |
1 |
32 |
1160 |
|
|
|
|
|
|
|
| 95 |
1 |
1 |
32 |
1192 |
|
|
|
|
|
|
|
| 96 |
1 |
1 |
33 |
1185 |
|
|
|
|
|
|
|
| 97 |
1 |
1 |
32 |
1192 |
|
|
|
|
|
|
|
| 98 |
1 |
1 |
33 |
1233 |
|
|
|
|
|
|
|
| 99 |
1 |
1 |
33 |
1267 |
|
|
|
|
|
|
|
| 100 |
1 |
1 |
34 |
1309 |
|
|
|
|
|
|
|
For more information have a look at this Preprint.
Back to the
LS MATHE II Homepage.
Sascha Kurz, February 2005.