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A275090 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

%I A275090 #4 Jul 16 2016 09:23:15
%S A275090 1,2,2,3,14,5,6,36,81,14,12,96,192,486,41,24,288,508,1024,2916,122,48,
%T A275090 864,1680,3088,5440,17496,365,96,2592,5304,12816,18440,29120,104976,
%U A275090 1094,192,7776,17184,53132,87924,111900,155904,629856,3281,384,23328,54484
%N A275090 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.
%C A275090 Table starts
%C A275090 ....1........2........3.........6.........12..........24............48
%C A275090 ....2.......14.......36........96........288.........864..........2592
%C A275090 ....5.......81......192.......508.......1680........5304.........17184
%C A275090 ...14......486.....1024......3088......12816.......53132........232156
%C A275090 ...41.....2916.....5440.....18440......87924......510680.......2934756
%C A275090 ..122....17496....29120....111900.....647648.....5038428......38872396
%C A275090 ..365...104976...155904....675600....4706400....48675088.....512150588
%C A275090 .1094...629856...834176...4094240...34281472...477786368....6767371752
%C A275090 .3281..3779136..4463424..24794560..248629316..4669603380...89090043684
%C A275090 .9842.22674816.23883904.150165020.1807849760.45596095332.1174911360788
%H A275090 R. H. Hardin, <a href="/A275090/b275090.txt">Table of n, a(n) for n = 1..336</a>
%F A275090 Empirical for column k:
%F A275090 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A275090 k=2: a(n) = 6*a(n-1) for n>3
%F A275090 k=3: [order 9] for n>10
%F A275090 k=4: [order 14] for n>15
%F A275090 k=5: [order 27] for n>28
%F A275090 k=6: [order 64] for n>66
%F A275090 Empirical for row n:
%F A275090 n=1: a(n) = 2*a(n-1) for n>3
%F A275090 n=2: a(n) = 3*a(n-1) for n>4
%F A275090 n=3: [order 36] for n>38
%F A275090 n=4: [order 84] for n>88
%e A275090 Some solutions for n=4 k=4
%e A275090 ..0..1..1..2. .0..1..2..0. .0..1..2..0. .0..0..1..2. .0..1..2..0
%e A275090 ..1..0..2..2. .0..2..2..0. .0..0..1..2. .0..0..1..2. .0..1..1..2
%e A275090 ..1..1..0..2. .0..2..2..1. .1..2..2..1. .0..1..1..2. .1..1..2..0
%e A275090 ..1..2..2..0. .0..1..1..0. .1..2..2..0. .0..2..1..0. .1..1..0..0
%Y A275090 Column 1 is A007051(n-1).
%Y A275090 Row 1 is A003945(n-2).
%K A275090 nonn,tabl
%O A275090 1,2
%A A275090 _R. H. Hardin_, Jul 16 2016