A385291 Square array read by descending antidiagonals: A(n,k) is the number of fixed n-dimensional polyominoes of size k.
1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 19, 15, 4, 1, 1, 63, 86, 28, 5, 1, 1, 216, 534, 234, 45, 6, 1, 1, 760, 3481, 2162, 495, 66, 7, 1, 1, 2725, 23502, 21272, 6095, 901, 91, 8, 1, 1, 9910, 162913, 218740, 80617, 13881, 1484, 120, 9, 1, 1, 36446, 1152870, 2323730, 1121075, 231008, 27468, 2276, 153, 10, 1
Offset: 1
Examples
The top corner of the array (size on horizontal axis, dimensions on vertical):
1: 1 1 1 1 1 1 1
(A001168) 2: 1 2 6 19 63 216 760
(A001931) 3: 1 3 15 86 534 3481 23502
(A151830) 4: 1 4 28 234 2162 21272 218740
(A151831) 5: 1 5 45 495 6095 80617 1121075
(A151832) 6: 1 6 66 901 13881 231008 4057660
(A151833) 7: 1 7 91 1484 27468 551313 11710328
(A151834) 8: 1 8 120 2276 49204 1156688 28831384
(A151835) 9: 1 9 153 3309 81837 2205489 63113061
10: 1 10 190 4615 128515 3906184 126210640
11: 1 11 231 6226 192786 6524265 234919234
12: 1 12 276 8174 278598 10389160 412504236
13: 1 13 325 10491 390299 15901145 690185431
14: 1 14 378 13209 532637 23538256 1108774772
15: 1 15 435 16360 710760 33863201 1720467820
16: 1 16 496 19976 930216 47530272 2590788848
17: 1 17 561 24089 1196953 65292257 3800689609
18: 1 18 630 28731 1517319 88007352 5448801768
19: 1 19 703 33934 1898062 116646073 7653842998
20: 1 20 780 39730 2346330 152298168 10557176740
21: 1 21 861 46151 2869671 196179529 14325525627
22: 1 22 946 53229 3476033 249639104 19153838572
23: 1 23 1035 60996 4173764 314165809 25268311520
24: 1 24 1128 69484 4971612 391395440 32929561864
Links
- John Mason, Table of n, a(n) for n = 1..162
Crossrefs
Formula
A(n,k) = Sum_{d=0..n} binomial(n,d)*A195739(k,d) (with A195739(k,d) = 0 for k <= d). - Pontus von Brömssen, Jun 28 2025
Extensions
a(56)-a(66) from Pontus von Brömssen, Jun 28 2025