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A241138 T(n,k)=Number of nXk 0..2 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..2 introduced in row major order.

%I A241138 #6 Jul 23 2025 11:11:54
%S A241138 0,1,1,1,2,1,2,5,5,2,3,17,24,17,3,6,56,152,152,56,6,11,195,935,1670,
%T A241138 935,195,11,22,691,6150,19619,19619,6150,691,22,43,2476,40504,238607,
%U A241138 434444,238607,40504,2476,43,86,8941,269481,2939027,9958520,9958520,2939027
%N A241138 T(n,k)=Number of nXk 0..2 arrays with no element equal to the same number of vertical neighbors as horizontal neighbors, with new values 0..2 introduced in row major order.
%C A241138 Table starts
%C A241138 ..0.....1........1..........2.............3..............6..............11
%C A241138 ..1.....2........5.........17............56............195.............691
%C A241138 ..1.....5.......24........152...........935...........6150...........40504
%C A241138 ..2....17......152.......1670.........19619.........238607.........2939027
%C A241138 ..3....56......935......19619........434444........9958520.......230889822
%C A241138 ..6...195.....6150.....238607.......9958520......428855442.....18742128588
%C A241138 .11...691....40504....2939027.....230889822....18742128588...1546330012544
%C A241138 .22..2476...269481...36470565....5392206371...825015103540.128518782423157
%C A241138 .43..8941..1797120..454209512..126282435834.36426835430201
%C A241138 .86.32393.12006500.5665536042.2961490680709
%H A241138 R. H. Hardin, <a href="/A241138/b241138.txt">Table of n, a(n) for n = 1..112</a>
%F A241138 Empirical for column k:
%F A241138 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) for n>4
%F A241138 k=2: a(n) = 4*a(n-1) +2*a(n-2) -11*a(n-3) -6*a(n-4) +8*a(n-5) for n>6
%F A241138 k=3: [order 26] for n>27
%e A241138 Some solutions for n=4 k=4
%e A241138 ..0..1..1..1....0..1..2..0....0..1..0..2....0..1..2..0....0..1..0..1
%e A241138 ..0..0..1..0....0..1..2..0....0..1..0..2....0..1..2..0....0..1..0..1
%e A241138 ..0..2..2..0....2..2..1..1....2..1..1..1....0..2..1..0....2..2..0..1
%e A241138 ..1..1..1..1....0..0..2..2....2..1..0..0....0..2..1..0....0..0..2..2
%Y A241138 Column 1 is A005578(n-2)
%K A241138 nonn,tabl
%O A241138 1,5
%A A241138 _R. H. Hardin_, Apr 16 2014