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%I #4 Dec 30 2016 20:56:24
%S 0,0,0,1,4,1,2,46,46,2,8,384,996,384,8,28,2894,16860,16860,2894,28,94,
%T 20444,259040,592416,259040,20444,94,304,138944,3753846,18844474,
%U 18844474,3753846,138944,304,960,918744,52433492,566131860,1240628942
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and vertical 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
%C ....0........4...........46............384............2894............20444
%C ....1.......46..........996..........16860..........259040..........3753846
%C ....2......384........16860.........592416........18844474........566131860
%C ....8.....2894.......259040.......18844474......1240628942......77217209188
%C ...28....20444......3753846......566131860.....77217209188....9962925424456
%C ...94...138944.....52433492....16393550046...4633270354464.1239330073038612
%C ..304...918744....713549156...462579750172.270955366695864
%C ..960..5954690...9525564453.12805032188772
%C .2976.38005496.125290653912
%H R. H. Hardin, <a href="/A280284/b280284.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7
%F k=2: [order 8]
%F k=3: [order 24] for n>25
%e Some solutions for n=3 k=4
%e ..0..1..0..2. .0..1..1..0. .0..0..1..2. .0..0..1..1. .0..1..2..0
%e ..2..0..1..2. .2..0..2..0. .2..1..2..2. .1..0..2..0. .2..2..0..1
%e ..2..0..0..1. .0..2..2..1. .0..2..1..1. .2..1..1..2. .0..1..0..0
%Y Column 2 is A279523.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 30 2016