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A224262 T(n,k) = number of n X k 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224262 #13 Mar 18 2025 16:05:34
%S A224262 3,9,6,22,36,10,46,158,100,15,86,548,648,225,21,148,1600,3096,2017,
%T A224262 441,28,239,4102,12032,12467,5246,784,36,367,9503,40182,59855,41012,
%U A224262 11990,1296,45,541,20299,119367,240829,238366,116692,24842,2025,55,771,40570
%N A224262 T(n,k) = number of n X k 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224262 R. H. Hardin, <a href="/A224262/b224262.txt">Table of n, a(n) for n = 1..241</a>
%F A224262 Empirical: columns k=1..7 are polynomials of order 2*k for n>0,0,0,2,4,6,8.
%F A224262 Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,0,2,4,6,8.
%e A224262 Table starts:
%e A224262    3    9     22      46       86       148        239         367          541
%e A224262    6   36    158     548     1600      4102       9503       20299        40570
%e A224262   10  100    648    3096    12032     40182     119367      322885       808618
%e A224262   15  225   2017   12467    59855    240829     850875     2717731      8000608
%e A224262   21  441   5246   41012   238366   1122522    4542734    16423026     54399996
%e A224262   28  784  11990  116692   816361   4480391   20568693    82733667    301228048
%e A224262   36 1296  24842  296646  2485967  15921905   83124099   371699763   1478187738
%e A224262   45 2025  47643  688533  6868203  51343083  306179180  1530419762   6671184875
%e A224262   55 3025  85838 1482310 17467782 152072846 1038489172  5835731860  28072690614
%e A224262   66 4356 146878 2995516 41364960 417672794 3266157979 20709405119 110622071553
%e A224262   ...
%e A224262 Some solutions for n=3 k=4:
%e A224262 ..1..1..0..0....1..1..1..1....1..1..2..1....0..2..1..0....0..0..0..0
%e A224262 ..2..1..1..0....1..2..2..1....2..2..2..1....0..2..1..1....0..0..2..0
%e A224262 ..2..2..1..1....2..2..2..1....2..2..2..2....0..2..2..1....0..0..2..2
%Y A224262 Main diagonal is A224256.
%Y A224262 Columns 1..7 are A000217(n+1), A000537(n+1), A224257, A224258, A224259, A224260, A224261.
%Y A224262 Rows 1..7 are A223718, A223919, A224263, A224264, A224265, A224266, A224267.
%Y A224262 Cf. A223838.
%K A224262 nonn,tabl
%O A224262 1,1
%A A224262 _R. H. Hardin_, Apr 02 2013
%E A224262 Name corrected by _Andrew Howroyd_, Mar 18 2025