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A202812 T(n,k) = Number of n X k nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.

%I A202812 #9 Oct 30 2014 05:03:33
%S A202812 1,1,1,1,3,1,1,6,6,1,1,10,32,10,1,1,15,121,121,15,1,1,21,356,1177,356,
%T A202812 21,1,1,28,881,8232,8232,881,28,1,1,36,1925,43483,146300,43483,1925,
%U A202812 36,1,1,45,3830,185051,1874539,1874539,185051,3830,45,1,1,55,7083,666610
%N A202812 T(n,k) = Number of n X k nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
%C A202812 Table starts:
%C A202812 .1..1.....1.......1..........1.............1................1
%C A202812 .1..3.....6......10.........15............21...............28
%C A202812 .1..6....32.....121........356...........881.............1925
%C A202812 .1.10...121....1177.......8232.........43483...........185051
%C A202812 .1.15...356....8232.....146300.......1874539.........17870566
%C A202812 .1.21...881...43483....1874539......60758779.......1420586923
%C A202812 .1.28..1925..185051...17870566....1420586923......83834499040
%C A202812 .1.36..3830..666610..133496644...24496279000....3569257400553
%C A202812 .1.45..7083.2105474..817995997..324818660255..111459151645204
%C A202812 .1.55.12352.5980085.4261304129.3450301922085.2641129540510016
%H A202812 R. H. Hardin, <a href="/A202812/b202812.txt">Table of n, a(n) for n = 1..312</a>
%F A202812 Empirical: columns of T(n,k) are polynomials in n of degree k*(k-1).
%F A202812 For elements increasing by 0..d instead of 0..2, columns are a polynomial of degree d*k*(k-1)/2.
%e A202812 Some solutions for n=5, k=3:
%e A202812 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A202812 ..0..0..0....0..0..0....0..0..1....0..0..0....0..0..2....0..0..2....0..0..1
%e A202812 ..0..0..0....0..0..2....0..2..2....0..0..1....0..2..2....0..1..2....0..0..2
%e A202812 ..0..0..1....0..2..2....0..2..2....0..2..3....0..2..3....0..1..2....0..0..2
%e A202812 ..0..0..1....0..2..4....0..2..2....0..2..3....0..2..4....0..2..4....0..0..2
%Y A202812 Column 2 is A000217.
%K A202812 nonn,tabl
%O A202812 1,5
%A A202812 _R. H. Hardin_, Dec 24 2011