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A297889
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero.
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8
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1, 2, 2, 4, 7, 4, 8, 13, 13, 8, 16, 29, 20, 29, 16, 32, 69, 26, 26, 69, 32, 64, 137, 41, 36, 41, 137, 64, 128, 301, 67, 84, 84, 67, 301, 128, 256, 705, 99, 134, 114, 134, 99, 705, 256, 512, 1461, 156, 223, 162, 162, 223, 156, 1461, 512, 1024, 3193, 255, 396, 248, 253, 248
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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..256..512.1024..2048..4096..8192..16384
...2....7..13..29..69.137.301.705.1461.3193.7373.15729.34405.78569.170813
...4...13..20..26..41..67..99.156..255..406..654..1075..1765..2903...4816
...8...29..26..36..84.134.223.396..638.1173.2157..3812..6922.12304..21936
..16...69..41..84.114.162.248.368..520..786.1308..2126..3136..5052...7740
..32..137..67.134.162.253.264.437..656..942.1308..2254..3113..4698...7376
..64..301..99.223.248.264.433.579..650.1124.1469..2441..3648..5209...7873
.128..705.156.396.368.437.579.734..864.1154.1711..2267..3028..4060...5423
.256.1461.255.638.520.656.650.864.1037.1248.1647..2362..2966..3994...5228
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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) -2*a(n-2) +8*a(n-3) -20*a(n-4) +8*a(n-5) for n>6
k=3: [order 10] for n>11
k=4: [order 30] for n>34
k=5: [order 86] for n>91
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EXAMPLE
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Some solutions for n=7 k=4
..0..1..1..0. .0..0..1..1. .0..1..0..0. .0..1..1..1. .0..1..0..0
..0..0..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..1..1
..1..1..0..0. .0..1..0..1. .0..0..0..1. .1..1..0..0. .1..0..0..0
..0..0..1..1. .1..1..0..0. .1..0..1..0. .1..1..0..0. .0..1..0..1
..1..0..0..0. .1..1..0..0. .1..0..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..1. .0..1..0..1. .0..0..0..1. .1..0..1..0. .0..1..0..1
..0..0..1..0. .1..1..0..0. .1..1..0..1. .0..1..0..1. .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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