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A241119 T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

%I A241119 #6 Jul 23 2025 11:10:46
%S A241119 1,2,2,5,15,5,15,178,178,15,51,2614,9918,2614,51,187,40148,587555,
%T A241119 587555,40148,187,715,622645,35000157,134229632,35000157,622645,715,
%U A241119 2795,9676364,2085879115,30679522712,30679522712,2085879115,9676364,2795
%N A241119 T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.
%C A241119 Table starts
%C A241119 ...1......2..........5............15................51..................187
%C A241119 ...2.....15........178..........2614.............40148...............622645
%C A241119 ...5....178.......9918........587555..........35000157...........2085879115
%C A241119 ..15...2614.....587555.....134229632.......30679522712........7012241396116
%C A241119 ..51..40148...35000157...30679522712....26891788727245....23571710809729613
%C A241119 .187.622645.2085879115.7012241396116.23571710809729613.79236581561126536192
%H A241119 R. H. Hardin, <a href="/A241119/b241119.txt">Table of n, a(n) for n = 1..84</a>
%F A241119 Empirical for column k:
%F A241119 k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
%F A241119 k=2: [order 8] for n>10
%F A241119 k=3: [order 20] for n>21
%F A241119 k=4: [order 74] for n>75
%e A241119 Some solutions for n=3 k=4
%e A241119 ..0..1..1..0....0..1..1..0....0..1..0..1....0..1..1..0....0..0..1..1
%e A241119 ..2..1..0..2....0..1..2..1....2..0..3..3....2..0..0..2....2..0..0..2
%e A241119 ..0..0..3..0....3..2..0..3....3..1..1..1....3..2..2..3....1..1..1..3
%Y A241119 Column 1 is A007581(n-1)
%Y A241119 Column 2 is A200795
%K A241119 nonn,tabl
%O A241119 1,2
%A A241119 _R. H. Hardin_, Apr 16 2014