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%I #4 Mar 08 2016 07:41:05
%S 0,7,7,84,900,84,756,36312,36312,756,6048,1213836,5695536,1213836,
%T 6048,45360,36926640,755009274,755009274,36926640,45360,326592,
%U 1064495604,91506078732,399002850360,91506078732,1064495604,326592,2286144
%N T(n,k)=Number of nXk 0..6 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling six exactly once.
%C Table starts
%C ........0..............7...................84.......................756
%C ........7............900................36312...................1213836
%C .......84..........36312..............5695536.................755009274
%C ......756........1213836............755009274..............399002850360
%C .....6048.......36926640..........91506078732...........193171242190020
%C ....45360.....1064495604.......10536802638018.........88942337408262936
%C ...326592....29614748232.....1172354654705496......39591200828582988102
%C ..2286144...803524526172...127313882431172946...17206536333078160595304
%C .15676416.21398721760608.13576906131836963556.7344924168583134203517654
%H R. H. Hardin, <a href="/A269937/b269937.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 12*a(n-1) -36*a(n-2)
%F k=2: [order 6] for n>7
%F k=3: [order 20] for n>21
%F k=4: [order 64] for n>65
%e Some solutions for n=2 k=4
%e ..0..3..1..6. .0..3..5..6. .0..0..0..5. .0..6..6..5. .0..2..2..6
%e ..1..1..0..2. .3..5..6..3. .4..4..1..4. .3..5..2..6. .4..1..3..2
%Y Column 1 is A269895.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 08 2016