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A303254
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T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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10
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0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1183, 361, 0, 13, 1934, 4556, 10264, 8664, 5918, 1172, 0, 21, 6861, 21843, 78679, 106803, 55624, 28680, 3809, 0, 34, 24386, 103319, 584333, 1218385, 1105676, 349273
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OFFSET
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1,5
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COMMENTS
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Table starts
.0.....1......1........2..........3...........5.............8..............13
.0.....3.....14.......45........146.........537..........1934............6861
.0....11.....49......203........955........4556.........21843..........103319
.0....34....250.....1401......10264.......78679........584333.........4330427
.0...111...1183.....8664.....106803.....1218385......13529019.......153269484
.0...361...5918....55624....1105676....19457754.....322544617......5622650429
.0..1172..28680...349273...11394429...306224454....7600681910....204093228252
.0..3809.141255..2229806..118856245..4895684572..181926316054...7516309079483
.0.12377.691968.14141138.1230109648.77683246701.4319287740641.274539947294004
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 43] for n>44
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 19] for n>21
n=4: [order 63] for n>66
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EXAMPLE
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Some solutions for n=5, k=4
..0..0..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..1. .0..0..1..0
..1..1..0..1. .1..0..0..0. .0..0..1..1. .0..1..0..0. .0..1..0..1
..1..0..0..0. .1..0..1..0. .0..1..0..0. .1..0..0..1. .0..0..1..1
..0..1..1..0. .0..1..1..1. .1..1..0..1. .1..1..1..1. .1..0..1..0
..0..0..0..1. .0..0..0..1. .1..0..1..1. .0..0..0..0. .0..1..0..1
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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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