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A268774 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%I A268774 #4 Feb 13 2016 08:28:28
%S A268774 0,3,3,12,12,12,36,32,32,36,96,100,112,100,96,240,248,446,446,248,240,
%T A268774 576,620,1524,2296,1524,620,576,1344,1456,5214,10340,10340,5214,1456,
%U A268774 1344,3072,3380,17000,46312,64112,46312,17000,3380,3072,6912,7656,54822
%N A268774 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%C A268774 Table starts
%C A268774 ....0.....3.....12.......36........96.........240..........576..........1344
%C A268774 ....3....12.....32......100.......248.........620.........1456..........3380
%C A268774 ...12....32....112......446......1524........5214........17000.........54822
%C A268774 ...36...100....446.....2296.....10340.......46312.......198114........837848
%C A268774 ...96...248...1524....10340.....64112......387146......2258084......12951796
%C A268774 ..240...620...5214....46312....387146.....3104544.....24222418.....185142872
%C A268774 ..576..1456..17000...198114...2258084....24222418....255353744....2624246370
%C A268774 .1344..3380..54822...837848..12951796...185142872...2624246370...36091542548
%C A268774 .3072..7656.173244..3472210..73011192..1393319226..26623649020..491176316484
%C A268774 .6912.17148.541910.14245712.406925194.10357051740.266457432340.6585970939900
%H A268774 R. H. Hardin, <a href="/A268774/b268774.txt">Table of n, a(n) for n = 1..612</a>
%F A268774 Empirical for column k:
%F A268774 k=1: a(n) = 4*a(n-1) -4*a(n-2)
%F A268774 k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F A268774 k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6) for n>8
%F A268774 k=4: [order 8] for n>10
%F A268774 k=5: [order 12] for n>14
%F A268774 k=6: [order 16] for n>18
%F A268774 k=7: [order 28] for n>30
%e A268774 Some solutions for n=4 k=4
%e A268774 ..2..1..2..2. .1..2..2..2. .0..0..0..0. .0..1..0..1. .2..2..1..2
%e A268774 ..1..2..2..1. .2..2..2..1. .1..0..1..0. .0..0..0..1. .2..2..2..2
%e A268774 ..2..2..2..2. .2..1..2..2. .0..0..0..0. .0..0..0..0. .1..2..2..2
%e A268774 ..2..1..2..1. .1..2..2..2. .1..1..0..1. .0..0..0..1. .2..1..2..2
%Y A268774 Column 1 is A167667(n-1).
%K A268774 nonn,tabl
%O A268774 1,2
%A A268774 _R. H. Hardin_, Feb 13 2016