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A268639 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

%I A268639 #4 Feb 09 2016 12:23:51
%S A268639 0,3,3,12,24,12,36,120,120,36,96,504,840,504,96,240,1944,5178,5178,
%T A268639 1944,240,576,7128,29772,47640,29772,7128,576,1344,25272,163878,
%U A268639 412740,412740,163878,25272,1344,3072,87480,875592,3440052,5419992,3440052,875592
%N A268639 T(n,k)=Number of nXk 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.
%C A268639 Table starts
%C A268639 ....0......3........12..........36............96.............240
%C A268639 ....3.....24.......120.........504..........1944............7128
%C A268639 ...12....120.......840........5178.........29772..........163878
%C A268639 ...36....504......5178.......47640........412740.........3440052
%C A268639 ...96...1944.....29772......412740.......5419992........68710116
%C A268639 ..240...7128....163878.....3440052......68710116......1328460312
%C A268639 ..576..25272....875592....27906474.....849572724.....25093766490
%C A268639 .1344..87480...4578186...221913216...10310685036....465757993812
%C A268639 .3072.297432..23548164..1737860310..123340687488...8527096170390
%C A268639 .6912.997272.119570574.13445785116.1458578214948.154406753980596
%H A268639 R. H. Hardin, <a href="/A268639/b268639.txt">Table of n, a(n) for n = 1..420</a>
%F A268639 Empirical for column k:
%F A268639 k=1: a(n) = 4*a(n-1) -4*a(n-2)
%F A268639 k=2: a(n) = 6*a(n-1) -9*a(n-2) for n>3
%F A268639 k=3: a(n) = 10*a(n-1) -29*a(n-2) +20*a(n-3) -4*a(n-4)
%F A268639 k=4: [order 6] for n>7
%F A268639 k=5: [order 10]
%F A268639 k=6: [order 14] for n>15
%F A268639 k=7: [order 26]
%e A268639 Some solutions for n=4 k=4
%e A268639 ..2..0..0..0. .2..2..1..0. .0..0..0..0. .2..1..2..2. .0..1..2..2
%e A268639 ..2..1..0..1. .2..1..0..0. .1..1..0..1. .2..2..1..0. .1..2..1..2
%e A268639 ..1..0..1..2. .2..0..1..0. .2..2..1..2. .2..1..0..1. .2..1..0..2
%e A268639 ..2..1..2..2. .2..1..0..1. .2..1..0..1. .1..2..1..2. .1..0..0..1
%Y A268639 Column 1 is A167667(n-1).
%K A268639 nonn,tabl
%O A268639 1,2
%A A268639 _R. H. Hardin_, Feb 09 2016