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A298917
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 5, 3, 3, 3, 5, 1, 1, 8, 5, 4, 4, 5, 8, 1, 1, 13, 8, 6, 7, 6, 8, 13, 1, 1, 21, 13, 9, 9, 9, 9, 13, 21, 1, 1, 34, 21, 14, 15, 14, 15, 14, 21, 34, 1, 1, 55, 34, 22, 26, 24, 24, 26, 22, 34, 55, 1, 1, 89, 55, 35, 46, 44, 40, 44, 46, 35, 55
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OFFSET
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1,12
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COMMENTS
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Table starts
.1..1..1..1..1..1...1...1...1....1....1.....1.....1......1......1.......1
.1..1..1..2..3..5...8..13..21...34...55....89...144....233....377.....610
.1..1..1..2..3..5...8..13..21...34...55....89...144....233....377.....610
.1..2..2..3..4..6...9..14..22...35...56....90...145....234....378.....611
.1..3..3..4..7..9..15..26..46...84..151...276...506....929...1708....3138
.1..5..5..6..9.14..24..44..81..156..306...602..1192...2370...4720....9415
.1..8..8..9.15.24..40..76.141..277..570..1171..2441...5157..10913...23193
.1.13.13.14.26.44..76.168.359..792.1895..4521.10886..26818..66131..163463
.1.21.21.22.46.81.141.359.873.2145.5971.16568.45898.131372.376833.1078872
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..612
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +a(n-2) for n>3
k=3: a(n) = a(n-1) +a(n-2) for n>3
k=4: a(n) = 2*a(n-1) -a(n-3)
k=5: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-5) -a(n-6) -a(n-7) -a(n-8) for n>9
k=6: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) -a(n-7) +2*a(n-8) for n>9
k=7: [order 14] for n>15
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EXAMPLE
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All solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0
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CROSSREFS
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Columns 2 and 3 are A000045(n-1).
Column 4 is A001611(n-1).
Sequence in context: A233867 A319814 A220272 * A322530 A303364 A131332
Adjacent sequences: A298914 A298915 A298916 * A298918 A298919 A298920
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 29 2018
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STATUS
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approved
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