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A299001
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 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, 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, 1502511, 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.....1502511......23031390.......353088569
..32...1841...39015....932318....23031390.....564821426.....13849577141
..64...7181..235033...8918662...353088569...13849577141....543022804167
.128..28010.1416220..85379274..5420414253..340272636359..21348528789475
.256.109255.8533123.817325435.83214520668.8360888694306.839394891016021
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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..1..1..0. .0..0..1..0. .0..0..1..0. .0..1..1..0. .0..1..1..0
..1..1..1..0. .1..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..1..0
..1..1..0..0. .1..1..0..1. .0..1..0..1. .1..1..0..1. .0..0..0..0
..0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..1..0. .1..1..0..1
..1..1..1..1. .1..0..0..1. .1..0..0..1. .1..0..0..0. .1..1..0..1
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A281831.
Sequence in context: A281837 A299081 A299844 * A299746 A299668 A300259
Adjacent sequences: A298998 A298999 A299000 * A299002 A299003 A299004
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 31 2018
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STATUS
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approved
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