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A299852
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T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 7 or 8 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, 26, 26, 8, 16, 88, 93, 88, 16, 32, 298, 357, 357, 298, 32, 64, 1012, 1401, 1626, 1401, 1012, 64, 128, 3440, 5533, 7770, 7770, 5533, 3440, 128, 256, 11700, 21764, 36968, 46799, 36968, 21764, 11700, 256, 512, 39804, 85620, 175258, 276154, 276154
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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.....26......88......298......1012........3440........11700
...4....26.....93.....357.....1401......5533.......21764........85620
...8....88....357....1626.....7770.....36968......175258.......831558
..16...298...1401....7770....46799....276154.....1620056......9548178
..32..1012...5533...36968...276154...2030211....14789406....108058244
..64..3440..21764..175258..1620056..14789406...133388471...1204666013
.128.11700..85620..831558..9548178.108058244..1204666013..13452150161
.256.39804.336966.3948404.56314168.790761211.10910971094.150810121407
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)
k=3: [order 16] for n>18
k=4: [order 64] for n>66
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EXAMPLE
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Some solutions for n=5, k=4
..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..1
..0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1. .0..0..1..0
..1..1..0..1. .0..1..0..1. .1..0..1..0. .1..1..0..1. .1..1..0..1
..1..0..0..1. .0..1..1..1. .1..0..0..1. .0..1..0..1. .0..1..0..1
..0..1..1..0. .0..0..1..0. .1..1..1..1. .0..1..0..0. .0..0..1..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A298189.
Sequence in context: A298195 A299089 A299345 * A299008 A299675 A299753
Adjacent sequences: A299849 A299850 A299851 * A299853 A299854 A299855
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 20 2018
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STATUS
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approved
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