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A223838 T(n,k) = number of n X k 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A223838 #11 Mar 18 2025 16:04:53
%S A223838 2,4,3,7,9,4,11,22,16,5,16,46,48,25,6,22,86,118,89,36,7,29,148,255,
%T A223838 249,149,49,8,37,239,503,596,471,232,64,9,46,367,926,1286,1240,824,
%U A223838 342,81,10,56,541,1614,2578,2884,2388,1356,483,100,11,67,771,2690,4886,6159,5992
%N A223838 T(n,k) = number of n X k 0..1 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A223838 R. H. Hardin, <a href="/A223838/b223838.txt">Table of n, a(n) for n = 1..477</a>
%F A223838 Empirical columns k=1..7 are polynomials of degree k for n>0,0,0,1,2,3,4.
%F A223838 Empirical rows n=1..7 are polynomials of degree 2*n for k>0,0,0,2,4,6,8.
%e A223838 Table starts:
%e A223838    2   4   7   11    16    22     29     37      46      56      67       79
%e A223838    3   9  22   46    86   148    239    367     541     771    1068     1444
%e A223838    4  16  48  118   255   503    926   1614    2690    4318    6712    10146
%e A223838    5  25  89  249   596  1286   2578   4886    8851   15439   26072    42800
%e A223838    6  36 149  471  1240  2884   6159  12371   23716   43790   78342   136368
%e A223838    7  49 232  824  2388  5992  13582  28642   57306  110164  205131   371923
%e A223838    8  64 342 1356  4325 11749  28369  62869  130891  260219  499470   932402
%e A223838    9  81 483 2123  7436 21912  56607 132427  287719  591705 1167798  2233350
%e A223838   10 100 659 3189 12222 39064 108282 268624  611901 1306407 2655964  5202806
%e A223838   11 121 874 4626 19316 66854 199047 525323 1260152 2805670 5897718 11863338
%e A223838   ...
%e A223838 Some solutions for n=3 k=4:
%e A223838 ..1..0..0..0....0..1..0..0....0..0..0..0....0..0..0..0....0..1..1..0
%e A223838 ..1..1..0..0....1..1..1..0....0..0..0..1....0..0..0..0....0..1..1..0
%e A223838 ..1..1..0..0....1..1..1..1....0..0..1..1....1..1..1..1....0..1..1..0
%Y A223838 Main diagonal is A223832.
%Y A223838 Columns 1..7 are A000027(n+1), A000290(n+1), A223833, A223834, A223835, A223836, A223837.
%Y A223838 Rows 1..7 are A000124, A223718, A223839, A223840, A223841, A223842, A223843.
%Y A223838 Cf. A224262, A224173.
%K A223838 nonn,tabl
%O A223838 1,1
%A A223838 _R. H. Hardin_, Mar 27 2013
%E A223838 Name corrected by _Andrew Howroyd_, Mar 18 2025