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A299746
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
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5
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1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 179, 121, 16, 32, 472, 1073, 1073, 472, 32, 64, 1841, 6479, 10150, 6479, 1841, 64, 128, 7181, 39015, 97462, 97462, 39015, 7181, 128, 256, 28010, 235033, 932318, 1502630, 932318, 235033, 28010, 256, 512, 109255, 1416220
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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
...2......8......31.......121.........472..........1841............7181
...4.....31.....179......1073........6479.........39015..........235033
...8....121....1073.....10150.......97462........932318.........8918662
..16....472....6479.....97462.....1502630......23034971.......353167830
..32...1841...39015....932318....23034971.....564998177.....13855907809
..64...7181..235033...8918662...353167830...13855907809....543386033722
.128..28010.1416220..85379274..5421997554..340475803209..21367169090398
.256.109255.8533123.817325435.83244577728.8367066746663.840301228632106
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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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
k=3: [order 10] for n>11
k=4: [order 37] for n>38
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..0..0. .0..0..0..1. .0..1..1..1
..0..1..1..0. .1..1..1..0. .0..0..1..0. .1..0..0..0. .1..0..0..0
..1..0..1..0. .0..0..0..1. .1..0..1..0. .0..0..1..0. .1..0..1..0
..1..0..0..1. .1..1..0..1. .0..0..1..0. .0..0..0..1. .0..0..1..1
..1..1..0..1. .1..1..1..0. .0..1..0..1. .1..1..1..1. .0..0..1..1
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A281831.
Column 3 is A298996.
Column 4 is A298997.
Sequence in context: A299081 A299844 A299001 * A299668 A300259 A305523
Adjacent sequences: A299743 A299744 A299745 * A299747 A299748 A299749
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 18 2018
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STATUS
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approved
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