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%I #4 Feb 08 2017 07:51:15
%S 0,0,0,0,0,0,0,1,1,0,0,8,44,8,0,0,104,2919,2919,104,0,0,1222,122866,
%T 418178,122866,1222,0,0,13552,4446172,48031921,48031921,4446172,13552,
%U 0,0,144784,148868304,4907541118,15775532484,4907541118,148868304,144784,0
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than four of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C .0........0............0..............0................0................0
%C .0........0............1..............8..............104.............1222
%C .0........1...........44...........2919...........122866..........4446172
%C .0........8.........2919.........418178.........48031921.......4907541118
%C .0......104.......122866.......48031921......15775532484....4628006363340
%C .0.....1222......4446172.....4907541118....4628006363340.3903552450233444
%C .0....13552....148868304...469203486998.1272857909584052
%C .0...144784...4745726158.42928015621172
%C .0..1506870.146320129628
%C .0.15382464
%H R. H. Hardin, <a href="/A282189/b282189.txt">Table of n, a(n) for n = 1..71</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 16*a(n-1) -48*a(n-2) -116*a(n-3) -160*a(n-4) -96*a(n-5) -36*a(n-6) for n>9
%F k=3: [order 30] for n>33
%e Some solutions for n=3 k=4
%e ..0..1..0..0. .0..1..1..0. .0..1..0..0. .0..0..1..0. .0..1..1..1
%e ..2..0..0..1. .1..2..2..2. .1..2..0..0. .0..0..0..1. .0..1..1..2
%e ..0..2..0..0. .1..2..2..2. .1..2..0..0. .1..0..1..0. .1..1..0..0
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Feb 08 2017
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