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A280233 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A280233 #4 Dec 29 2016 11:50:26
%S A280233 0,0,0,2,4,2,2,6,6,2,5,8,9,8,5,8,14,16,16,14,8,15,24,29,48,29,24,15,
%T A280233 26,42,52,116,116,52,42,26,46,72,95,288,355,288,95,72,46,80,124,168,
%U A280233 678,1102,1102,678,168,124,80,139,212,298,1600,3376,4260,3376,1600,298,212
%N A280233 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C A280233 Table starts
%C A280233 ..0...0...2....2.....5......8......15.......26........46.........80.........139
%C A280233 ..0...4...6....8....14.....24......42.......72.......124........212.........362
%C A280233 ..2...6...9...16....29.....52......95......168.......298........522.........911
%C A280233 ..2...8..16...48...116....288.....678.....1600......3766.......8704.......20040
%C A280233 ..5..14..29..116...355...1102....3376.....9860.....29091......84644......244759
%C A280233 ..8..24..52..288..1102...4260...16282....59648....220330.....806580.....2928596
%C A280233 .15..42..95..678..3376..16282...80825...377706...1780344....8321484....38431266
%C A280233 .26..72.168.1600..9860..59648..377706..2212304..13139746...77599244...451789710
%C A280233 .46.124.298.3766.29091.220330.1780344.13139746..98743448..738470180..5428286449
%C A280233 .80.212.522.8704.84644.806580.8321484.77599244.738470180.7008698040.65195901946
%H A280233 R. H. Hardin, <a href="/A280233/b280233.txt">Table of n, a(n) for n = 1..220</a>
%F A280233 Empirical for column k:
%F A280233 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F A280233 k=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>7
%F A280233 k=3: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>7
%F A280233 k=4: [order 16] for n>19
%F A280233 k=5: [order 22] for n>25
%e A280233 Some solutions for n=4 k=4
%e A280233 ..0..0..0..1. .0..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e A280233 ..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
%e A280233 ..0..0..0..0. .1..1..1..1. .0..0..1..0. .1..1..1..1. .1..0..0..0
%e A280233 ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
%Y A280233 Column 1 is A006367(n-1).
%K A280233 nonn,tabl
%O A280233 1,4
%A A280233 _R. H. Hardin_, Dec 29 2016