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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 6

%I #4 Apr 16 2014 11:14:11

%S 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 935,195,11,22,691,6150,19619,19619,6150,691,22,43,2476,40504,238607,

%U 434444,238607,40504,2476,43,86,8941,269481,2939027,9958520,9958520,2939027

%N 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 Table starts

%C ..0.....1........1..........2.............3..............6..............11

%C ..1.....2........5.........17............56............195.............691

%C ..1.....5.......24........152...........935...........6150...........40504

%C ..2....17......152.......1670.........19619.........238607.........2939027

%C ..3....56......935......19619........434444........9958520.......230889822

%C ..6...195.....6150.....238607.......9958520......428855442.....18742128588

%C .11...691....40504....2939027.....230889822....18742128588...1546330012544

%C .22..2476...269481...36470565....5392206371...825015103540.128518782423157

%C .43..8941..1797120..454209512..126282435834.36426835430201

%C .86.32393.12006500.5665536042.2961490680709

%H R. H. Hardin, <a href="/A241138/b241138.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) for n>4

%F 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 k=3: [order 26] for n>27

%e Some solutions for n=4 k=4

%e ..0..1..1..1....0..1..2..0....0..1..0..2....0..1..2..0....0..1..0..1

%e ..0..0..1..0....0..1..2..0....0..1..0..2....0..1..2..0....0..1..0..1

%e ..0..2..2..0....2..2..1..1....2..1..1..1....0..2..1..0....2..2..0..1

%e ..1..1..1..1....0..0..2..2....2..1..0..0....0..2..1..0....0..0..2..2

%Y Column 1 is A005578(n-2)

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 16 2014

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Last modified April 15 12:10 EDT 2024. Contains 371681 sequences. (Running on oeis4.)