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A305457
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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5
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0, 0, 0, 0, 3, 0, 0, 5, 5, 0, 0, 18, 14, 18, 0, 0, 61, 69, 69, 61, 0, 0, 209, 376, 661, 376, 209, 0, 0, 702, 1891, 5580, 5580, 1891, 702, 0, 0, 2381, 9889, 48148, 79810, 48148, 9889, 2381, 0, 0, 8069, 51283, 418382, 1117343, 1117343, 418382, 51283, 8069, 0, 0, 27330
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OFFSET
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1,5
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COMMENTS
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Table starts
.0....0......0........0..........0............0..............0................0
.0....3......5.......18.........61..........209............702.............2381
.0....5.....14.......69........376.........1891...........9889............51283
.0...18.....69......661.......5580........48148.........418382..........3621421
.0...61....376.....5580......79810......1117343.......16062787........228184784
.0..209...1891....48148....1117343.....25891309......612656116......14339915102
.0..702...9889...418382...16062787....612656116....23996865179.....926180069711
.0.2381..51283..3621421..228184784..14339915102...926180069711...58862515324951
.0.8069.265582.31403562.3255027240.337239061289.35989846262523.3770741435617783
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
k=3: [order 14] for n>16
k=4: [order 42] for n>43
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..0..1..1. .0..0..1..0. .0..1..0..1
..1..1..1..0. .1..1..0..1. .1..1..0..0. .1..1..1..1. .1..0..1..0
..0..0..0..1. .1..0..1..1. .0..1..0..0. .0..0..0..1. .0..1..1..0
..1..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..0..0. .1..0..0..1
..0..1..0..1. .1..1..0..1. .0..0..0..0. .0..1..1..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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