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A305776
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 23, 23, 8, 16, 65, 81, 65, 16, 32, 192, 292, 292, 192, 32, 64, 569, 1096, 1481, 1096, 569, 64, 128, 1709, 4172, 7528, 7528, 4172, 1709, 128, 256, 5162, 15953, 38623, 51586, 38623, 15953, 5162, 256, 512, 15663, 61111, 199257, 362200, 362200
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OFFSET
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1,2
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COMMENTS
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Table starts
...1.....2......4.......8........16.........32..........64...........128
...2.....8.....23......65.......192........569........1709..........5162
...4....23.....81.....292......1096.......4172.......15953.........61111
...8....65....292....1481......7528......38623......199257.......1028731
..16...192...1096....7528.....51586.....362200.....2553685......18030904
..32...569...4172...38623....362200....3492739....33891076.....329477646
..64..1709..15953..199257...2553685...33891076...453853629....6095547869
.128..5162..61111.1028731..18030904..329477646..6095547869..113299205109
.256.15663.234288.5312551.127390570.3206311981.81987206051.2110390711467
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5
k=3: [order 16]
k=4: [order 57] for n>59
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..1
..1..1..0..0. .1..1..1..1. .1..1..1..0. .1..1..0..0. .1..0..1..1
..1..0..1..1. .0..0..1..0. .1..0..0..0. .1..1..1..0. .0..1..0..1
..1..1..1..1. .1..0..0..0. .0..0..1..0. .1..1..1..1. .0..1..0..0
..1..0..1..0. .0..0..0..1. .1..0..0..1. .0..1..1..0. .0..1..1..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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