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%I #4 Jan 26 2017 07:20:46
%S 0,0,0,1,4,0,2,70,46,0,8,400,985,384,0,28,2128,7986,10572,2894,0,94,
%T 10512,67884,135444,104815,20444,0,304,49352,519656,1887730,2159590,
%U 982206,138944,0,960,225024,3804074,23075928,48871479,32771472,8921869
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C .0........0..........1...........2............8............28............94
%C .0........4.........70.........400.........2128.........10512.........49352
%C .0.......46........985........7986........67884........519656.......3804074
%C .0......384......10572......135444......1887730......23075928.....270969324
%C .0.....2894.....104815.....2159590.....48871479.....955490042...18092139475
%C .0....20444.....982206....32771472...1205962480...37763465272.1154703692514
%C .0...138944....8921869...483655876..28906723792.1449940771656
%C .0...918744...79152992..6987992320.677956602812
%C .0..5954690..690169163.99358947608
%C .0.38005496.5936924514
%H R. H. Hardin, <a href="/A281653/b281653.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: [order 8]
%F k=3: [order 10] for n>13
%F k=4: [order 32] for n>37
%F Empirical for row n:
%F n=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7
%F n=2: [order 8] for n>9
%F n=3: [order 26] for n>29
%e Some solutions for n=4 k=4
%e ..0..1..0..2. .0..1..0..0. .0..1..0..2. .0..0..1..2. .0..1..0..1
%e ..2..1..1..1. .0..2..2..1. .0..2..0..2. .1..1..1..2. .2..0..2..1
%e ..0..0..2..1. .0..2..0..0. .1..0..1..2. .2..0..2..0. .0..1..0..2
%e ..2..1..2..1. .0..2..1..1. .2..0..1..2. .1..1..2..0. .1..2..0..2
%Y Column 2 is A279523.
%Y Row 1 is A280279.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 26 2017
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