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%I #4 Feb 10 2017 14:56:10
%S 1,2,2,5,14,5,14,121,121,14,41,1085,2992,1085,41,122,9729,75413,75413,
%T 9729,122,365,87238,1899634,5432319,1899634,87238,365,1094,782246,
%U 47863268,390546284,390546284,47863268,782246,1094,3281,7014246
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ...1......2..........5............14...............41.................122
%C ...2.....14........121..........1085.............9729...............87238
%C ...5....121.......2992.........75413..........1899634............47863268
%C ..14...1085......75413.......5432319........390546284.........28094166670
%C ..41...9729....1899634.....390546284......80034513705......16416580121620
%C .122..87238...47863268...28094166670...16416580121620....9604952929717842
%C .365.782246.1205981686.2020997096826.3367389843804209.5619690409304729594
%H R. H. Hardin, <a href="/A282275/b282275.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) -3*a(n-2)
%F k=2: a(n) = 8*a(n-1) +8*a(n-2) +6*a(n-3) for n>5
%F k=3: [order 10] for n>11
%F k=4: [order 29] for n>30
%e Some solutions for n=3 k=4
%e ..0..1..0..1. .0..0..0..1. .0..1..2..0. .0..1..1..2. .0..1..0..0
%e ..2..2..0..1. .2..2..1..1. .2..1..2..2. .0..1..2..0. .0..0..0..1
%e ..1..2..1..2. .0..1..1..0. .0..1..2..0. .1..2..1..0. .2..1..2..1
%Y Column 1 is A007051(n-1).
%Y Column 2 is A206628(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 10 2017
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