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A305642
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 29, 28, 16, 32, 94, 78, 78, 94, 32, 64, 284, 255, 334, 255, 284, 64, 128, 752, 743, 1516, 1516, 743, 752, 128, 256, 2244, 2197, 6329, 8734, 6329, 2197, 2244, 256, 512, 6532, 6663, 27110, 48567, 48567, 27110, 6663, 6532, 512
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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
...2....4....14.....28.......94.......284........752.........2244
...4...14....29.....78......255.......743.......2197.........6663
...8...28....78....334.....1516......6329......27110.......118085
..16...94...255...1516.....8734.....48567.....282463......1774950
..32..284...743...6329....48567....385282....3252937.....29925524
..64..752..2197..27110...282463...3252937...42274045....591351392
.128.2244..6663.118085..1774950..29925524..591351392..12972861669
.256.6532.20052.519355.11228442.280854245.8584480725.293775609320
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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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
k=3: [order 15] for n>17
k=4: [order 65] for n>67
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..1
..0..0..0..1. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..1..0..0..0. .1..1..0..0. .1..1..1..1. .0..0..0..1. .0..0..0..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A304341.
Sequence in context: A193916 A304347 A316218 * A317036 A305911 A317153
Adjacent sequences: A305639 A305640 A305641 * A305643 A305644 A305645
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jun 07 2018
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STATUS
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approved
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