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A269052 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

%I A269052 #4 Feb 18 2016 11:38:51
%S A269052 3,9,9,24,42,27,60,102,174,81,144,360,594,666,243,336,1068,3078,3258,
%T A269052 2430,729,768,3288,13140,24192,17346,8586,2187,1728,9864,58752,149358,
%U A269052 183072,90450,29646,6561,3840,29472,253416,971844,1643376,1350672,464250
%N A269052 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.
%C A269052 Table starts
%C A269052 .....3.......9.......24.........60..........144............336.............768
%C A269052 .....9......42......102........360.........1068...........3288............9864
%C A269052 ....27.....174......594.......3078........13140..........58752..........253416
%C A269052 ....81.....666.....3258......24192.......149358.........971844.........6053094
%C A269052 ...243....2430....17346.....183072......1643376.......15547380.......140497512
%C A269052 ...729....8586....90450....1350672.....17696520......242861616......3193266318
%C A269052 ..2187...29646...464250....9779808....187575858.....3726221592.....71430596250
%C A269052 ..6561..100602..2353338...69793968...1964080920....56376679620...1577976495486
%C A269052 .19683..336798.11809746..492374976..20365312416...843461153880..34509932303172
%C A269052 .59049.1115370.58773858.3441051984.209472681102.12504078167988.748499855355192
%H A269052 R. H. Hardin, <a href="/A269052/b269052.txt">Table of n, a(n) for n = 1..337</a>
%F A269052 Empirical for column k:
%F A269052 k=1: a(n) = 3*a(n-1)
%F A269052 k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
%F A269052 k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4) for n>5
%F A269052 k=4: a(n) = 14*a(n-1) -57*a(n-2) +56*a(n-3) -16*a(n-4) for n>5
%F A269052 k=5: [order 12] for n>13
%F A269052 k=6: [order 18] for n>19
%F A269052 k=7: [order 38] for n>39
%F A269052 Empirical for row n:
%F A269052 n=1: a(n) = 4*a(n-1) -4*a(n-2)
%F A269052 n=2: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4)
%F A269052 n=3: a(n) = 6*a(n-1) -a(n-2) -28*a(n-3) -4*a(n-4) +16*a(n-5) -4*a(n-6) for n>8
%F A269052 n=4: [order 12] for n>14
%F A269052 n=5: [order 20] for n>22
%F A269052 n=6: [order 46] for n>48
%F A269052 n=7: [order 92] for n>94
%e A269052 Some solutions for n=4 k=4
%e A269052 ..1..2..2..1. .1..2..1..0. .0..1..2..2. .0..1..0..1. .2..1..0..1
%e A269052 ..2..2..2..1. .1..2..1..0. .2..1..2..1. .0..1..2..1. .2..1..2..1
%e A269052 ..1..2..2..2. .1..0..1..2. .1..2..2..1. .2..1..0..1. .2..1..2..1
%e A269052 ..1..2..1..2. .0..2..1..2. .1..2..2..2. .0..1..2..0. .2..1..2..1
%Y A269052 Column 1 is A000244.
%Y A269052 Column 2 is A268622.
%Y A269052 Row 1 is A084858.
%K A269052 nonn,tabl
%O A269052 1,1
%A A269052 _R. H. Hardin_, Feb 18 2016