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A303719
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 5, 5, 8, 13, 7, 8, 8, 7, 13, 21, 13, 14, 17, 14, 13, 21, 34, 23, 24, 36, 36, 24, 23, 34, 55, 37, 40, 76, 81, 76, 40, 37, 55, 89, 63, 68, 161, 169, 169, 161, 68, 63, 89, 144, 109, 116, 349, 361, 343, 361, 349, 116, 109, 144, 233, 183, 196, 749
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OFFSET
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1,2
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COMMENTS
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Table starts
..1..2...3...5....8...13...21....34....55....89....144....233....377.....610
..2..1...3...5....7...13...23....37....63...109....183....309....527.....893
..3..3...5...8...14...24...40....68...116...196....332....564....956....1620
..5..5...8..17...36...76..161...349...749..1604...3449...7412..15912...34177
..8..7..14..36...81..169..361...784..1681..3600...7744..16641..35721...76729
.13.13..24..76..169..343..741..1618..3451..7390..15924..34201..73387..157681
.21.23..40.161..361..741.1592..3469..7416.15880..34193..73457.157645..338676
.34.37..68.349..784.1618.3469..7551.16159.34602..74481.160024.343450..737809
.55.63.116.749.1681.3451.7416.16159.34546.73974.159281.342185.734359.1577656
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..6123
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FORMULA
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Empirical for diagonal:
Diagonal: [linear recurrence of order 15] for n>18
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +2*a(n-3) for n>4
k=3: a(n) = a(n-1) +2*a(n-3) for n>4
k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
k=5: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
k=6: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
k=7: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9
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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..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0
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CROSSREFS
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Column 1 is A000045(n+1).
Column 2 is A003229(n-1).
Sequence in context: A059897 A325821 A341607 * A299595 A304270 A318545
Adjacent sequences: A303716 A303717 A303718 * A303720 A303721 A303722
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Apr 29 2018
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STATUS
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approved
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