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A275090
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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.
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12
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1, 2, 2, 3, 14, 5, 6, 36, 81, 14, 12, 96, 192, 486, 41, 24, 288, 508, 1024, 2916, 122, 48, 864, 1680, 3088, 5440, 17496, 365, 96, 2592, 5304, 12816, 18440, 29120, 104976, 1094, 192, 7776, 17184, 53132, 87924, 111900, 155904, 629856, 3281, 384, 23328, 54484
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OFFSET
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1,2
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COMMENTS
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Table starts
....1........2........3.........6.........12..........24............48
....2.......14.......36........96........288.........864..........2592
....5.......81......192.......508.......1680........5304.........17184
...14......486.....1024......3088......12816.......53132........232156
...41.....2916.....5440.....18440......87924......510680.......2934756
..122....17496....29120....111900.....647648.....5038428......38872396
..365...104976...155904....675600....4706400....48675088.....512150588
.1094...629856...834176...4094240...34281472...477786368....6767371752
.3281..3779136..4463424..24794560..248629316..4669603380...89090043684
.9842.22674816.23883904.150165020.1807849760.45596095332.1174911360788
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1) for n>3
k=3: [order 9] for n>10
k=4: [order 14] for n>15
k=5: [order 27] for n>28
k=6: [order 64] for n>66
Empirical for row n:
n=1: a(n) = 2*a(n-1) for n>3
n=2: a(n) = 3*a(n-1) for n>4
n=3: [order 36] for n>38
n=4: [order 84] for n>88
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..1..2. .0..1..2..0. .0..1..2..0. .0..0..1..2. .0..1..2..0
..1..0..2..2. .0..2..2..0. .0..0..1..2. .0..0..1..2. .0..1..1..2
..1..1..0..2. .0..2..2..1. .1..2..2..1. .0..1..1..2. .1..1..2..0
..1..2..2..0. .0..1..1..0. .1..2..2..0. .0..2..1..0. .1..1..0..0
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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