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%I #4 Mar 09 2016 07:20:52
%S 0,5,5,40,240,40,240,5400,5400,240,1280,99840,385200,99840,1280,6400,
%T 1683240,22911300,22911300,1683240,6400,30720,26891280,1248460920,
%U 4410058320,1248460920,26891280,30720,143360,414705720,64599504300
%N T(n,k)=Number of nXk 0..4 arrays with some element plus some horizontally or vertically adjacent neighbor totalling four exactly once.
%C Table starts
%C ......0...........5...............40...................240
%C ......5.........240.............5400.................99840
%C .....40........5400...........385200..............22911300
%C ....240.......99840.........22911300............4410058320
%C ...1280.....1683240.......1248460920..........779206497960
%C ...6400....26891280......64599504300.......130850370606120
%C ..30720...414705720....3230189811360.....21244602958557060
%C .143360..6237722400..157641639369300...3367363526042121600
%C .655360.92095515720.7554828673749960.524230216822482202860
%H R. H. Hardin, <a href="/A270058/b270058.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) -16*a(n-2)
%F k=2: a(n) = 26*a(n-1) -169*a(n-2) for n>3
%F k=3: a(n) = 90*a(n-1) -2257*a(n-2) +10440*a(n-3) -13456*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
%F k=7: [order 64] for n>65
%e Some solutions for n=2 k=4
%e ..4..3..1..0. .2..1..0..2. .3..3..4..3. .0..3..1..2. .0..3..4..3
%e ..3..3..0..0. .1..4..0..1. .2..1..2..4. .1..0..1..0. .0..4..2..3
%Y Column 1 is A269822.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 09 2016
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