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A269902 T(n,k)=Number of nXk 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once. 9

%I

%S 0,7,7,84,840,84,756,45360,45360,756,6048,2005080,12377400,2005080,

%T 6048,45360,80724000,2801265390,2801265390,80724000,45360,326592,

%U 3078006120,579818225700,3263186052840,579818225700,3078006120,326592,2286144

%N T(n,k)=Number of nXk 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.

%C Table starts

%C .....0..........7..............84.................756.....................6048

%C .....7........840...........45360.............2005080.................80724000

%C ....84......45360........12377400..........2801265390.............579818225700

%C ...756....2005080......2801265390.......3263186052840.........3482459146452300

%C ..6048...80724000....579818225700....3482459146452300.....19179756370570398120

%C .45360.3078006120.113873466835170.3529041005211929340.100348236778061082424740

%H R. H. Hardin, <a href="/A269902/b269902.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 12*a(n-1) -36*a(n-2)

%F k=2: a(n) = 62*a(n-1) -961*a(n-2) for n>3

%F k=3: a(n) = 330*a(n-1) -28773*a(n-2) +255420*a(n-3) -599076*a(n-4) for n>5

%F k=4: [order 6] for n>7

%F k=5: [order 14] for n>15

%F k=6: [order 26] for n>27

%e Some solutions for n=2 k=4

%e ..2..4..3..2. .3..3..4..4. .3..4..3..6. .5..3..3..0. .2..3..4..5

%e ..0..4..5..2. .0..5..4..0. .0..5..3..1. .0..2..6..4. .0..2..4..3

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Mar 07 2016

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Last modified January 29 01:46 EST 2020. Contains 331328 sequences. (Running on oeis4.)