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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.
12
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
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
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
EXAMPLE
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
CROSSREFS
Column 1 is A007051(n-1).
Row 1 is A003945(n-2).
Sequence in context: A338523 A189312 A275565 * A373310 A274983 A153938
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 16 2016
STATUS
approved