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%I #4 Mar 28 2014 08:41:54
%S 2,3,3,4,8,4,5,17,17,5,6,35,68,35,6,7,64,244,244,64,7,8,109,777,1613,
%T 777,109,8,9,176,2221,9066,9066,2221,176,9,10,272,5853,46260,94613,
%U 46260,5853,272,10,11,405,14488,214126,874352,874352,214126,14488,405,11,12
%N T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4
%C Table starts
%C ..2...3.....4........5..........6...........7............8............9
%C ..3...8....17.......35.........64.........109..........176..........272
%C ..4..17....68......244........777........2221.........5853........14488
%C ..5..35...244.....1613.......9066.......46260.......214126.......921674
%C ..6..64...777.....9066......94613......874352......7359682.....57010666
%C ..7.109..2221....46260.....874352....15039319....232886648...3315673203
%C ..8.176..5853...214126....7359682...232886648...6712505927.177152281120
%C ..9.272.14488...921674...57010666..3315673203.177152281120
%C .10.405.34057..3745690..415293446.44101959522
%C .11.584.76495.14493362.2875073417
%H R. H. Hardin, <a href="/A239849/b239849.txt">Table of n, a(n) for n = 1..112</a>
%F Empirical for column k:
%F k=1: a(n) = n + 1
%F k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (53/12)*n - 6 for n>2
%F k=3: [polynomial of degree 13] for n>9
%F k=4: [polynomial of degree 40] for n>31
%F k=5: [polynomial of degree 121] for n>98
%e Some solutions for n=4 k=4
%e ..0..0..0..0....0..0..0..3....3..3..0..0....0..0..0..0....0..0..3..3
%e ..0..0..0..3....3..3..0..1....3..2..3..3....0..3..3..0....0..3..3..2
%e ..0..0..3..1....3..2..3..0....0..0..2..1....0..3..2..0....3..1..2..0
%e ..0..0..3..2....0..3..1..3....0..3..3..0....0..0..3..2....3..2..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 28 2014
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