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A298221
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 5 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, 73, 40, 40, 73, 32, 64, 157, 89, 120, 89, 157, 64, 128, 353, 195, 503, 503, 195, 353, 128, 256, 869, 451, 1492, 2066, 1492, 451, 869, 256, 512, 1993, 1046, 4767, 6598, 6598, 4767, 1046, 1993, 512, 1024, 4557, 2453
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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
...2....7...13....29.....73.....157......353.......869.......1993........4557
...4...13...20....40.....89.....195......451......1046.......2453........5810
...8...29...40...120....503....1492.....4767.....17127......56292......185937
..16...73...89...503...2066....6598....30780....125759.....498466.....2153157
..32..157..195..1492...6598...25717...150617....749072....3768994....20393224
..64..353..451..4767..30780..150617..1261845...8555774...57269902...425814658
.128..869.1046.17127.125759..749072..8555774..72407248..624571738..6148262835
.256.1993.2453.56292.498466.3768994.57269902.624571738.7205019743.93491026869
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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) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
k=3: [order 14] for n>15
k=4: [order 62] for n>65
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EXAMPLE
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Some solutions for n=6 k=4
..0..0..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..0..1..0
..1..1..0..0. .1..1..0..1. .1..0..1..0. .1..0..0..1. .1..0..1..1
..0..1..1..1. .0..0..0..0. .0..0..1..0. .0..0..1..0. .1..0..0..0
..0..1..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..0. .1..0..0..1
..1..0..1..1. .0..1..0..1. .1..0..1..1. .1..0..0..1. .0..1..1..0
..0..1..0..0. .0..0..0..1. .0..0..1..0. .0..1..0..1. .1..1..1..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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