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A316686
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4, 5, 7 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, 73, 73, 61, 0, 0, 209, 387, 769, 387, 209, 0, 0, 702, 2000, 6742, 6742, 2000, 702, 0, 0, 2381, 10487, 62314, 101803, 62314, 10487, 2381, 0, 0, 8069, 54957, 570806, 1591947, 1591947, 570806, 54957, 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....3......5.......18.........61..........209.............702
.0....5.....14.......73........387.........2000...........10487
.0...18.....73......769.......6742........62314..........570806
.0...61....387.....6742.....101803......1591947........24891152
.0..209...2000....62314....1591947.....43037698......1155724711
.0..702..10487...570806...24891152...1155724711.....53245963290
.0.2381..54957..5242925..389069291..31086640568...2457712512055
.0.8069.287218.48153854.6084616648.836374058655.113464874364839
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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) = 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 15] for n>16
k=4: [order 42] for n>44
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..1..0
..1..1..1..1. .1..1..1..1. .0..1..0..0. .1..1..0..1. .1..0..0..1
..0..0..1..0. .0..1..0..0. .1..1..0..0. .0..1..1..0. .0..0..0..1
..0..0..1..1. .1..0..0..0. .0..1..1..1. .0..0..1..0. .0..1..1..0
..1..1..0..0. .1..0..1..1. .1..0..0..0. .1..0..1..0. .1..0..1..0
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CROSSREFS
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Column 2 is A303684.
Column 3 is A305017.
Column 4 is A305018.
Sequence in context: A304065 A305457 A305022 * A304767 A316511 A317465
Adjacent sequences: A316683 A316684 A316685 * A316687 A316688 A316689
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jul 10 2018
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STATUS
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approved
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