A223838 T(n,k) = number of n X k 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
2, 4, 3, 7, 9, 4, 11, 22, 16, 5, 16, 46, 48, 25, 6, 22, 86, 118, 89, 36, 7, 29, 148, 255, 249, 149, 49, 8, 37, 239, 503, 596, 471, 232, 64, 9, 46, 367, 926, 1286, 1240, 824, 342, 81, 10, 56, 541, 1614, 2578, 2884, 2388, 1356, 483, 100, 11, 67, 771, 2690, 4886, 6159, 5992
Offset: 1
Examples
Table starts: 2 4 7 11 16 22 29 37 46 56 67 79 3 9 22 46 86 148 239 367 541 771 1068 1444 4 16 48 118 255 503 926 1614 2690 4318 6712 10146 5 25 89 249 596 1286 2578 4886 8851 15439 26072 42800 6 36 149 471 1240 2884 6159 12371 23716 43790 78342 136368 7 49 232 824 2388 5992 13582 28642 57306 110164 205131 371923 8 64 342 1356 4325 11749 28369 62869 130891 260219 499470 932402 9 81 483 2123 7436 21912 56607 132427 287719 591705 1167798 2233350 10 100 659 3189 12222 39064 108282 268624 611901 1306407 2655964 5202806 11 121 874 4626 19316 66854 199047 525323 1260152 2805670 5897718 11863338 ... Some solutions for n=3 k=4: ..1..0..0..0....0..1..0..0....0..0..0..0....0..0..0..0....0..1..1..0 ..1..1..0..0....1..1..1..0....0..0..0..1....0..0..0..0....0..1..1..0 ..1..1..0..0....1..1..1..1....0..0..1..1....1..1..1..1....0..1..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..477
Crossrefs
Formula
Empirical columns k=1..7 are polynomials of degree k for n>0,0,0,1,2,3,4.
Empirical rows n=1..7 are polynomials of degree 2*n for k>0,0,0,2,4,6,8.
Extensions
Name corrected by Andrew Howroyd, Mar 18 2025