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A298187
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
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4
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 3, 3, 5, 0, 0, 8, 5, 4, 4, 5, 8, 0, 0, 13, 8, 6, 5, 6, 8, 13, 0, 0, 21, 13, 9, 7, 7, 9, 13, 21, 0, 0, 34, 21, 14, 10, 10, 10, 14, 21, 34, 0, 0, 55, 34, 22, 15, 14, 14, 15, 22, 34, 55, 0, 0, 89, 55, 35, 23, 20, 19, 20, 23, 35, 55
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OFFSET
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1,12
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COMMENTS
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Table starts
.0..0..0..0..0..0..0..0..0...0...0...0...0....0....0....0....0.....0.....0
.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584
.0..1..1..2..3..5..8.13.21..34..55..89.144..233..377..610..987..1597..2584
.0..2..2..3..4..6..9.14.22..35..56..90.145..234..378..611..988..1598..2585
.0..3..3..4..5..7.10.15.23..36..57..91.146..235..379..612..989..1599..2586
.0..5..5..6..7.10.14.20.29..44..68.106.166..262..416..663.1059..1695..2718
.0..8..8..9.10.14.19.27.38..58..90.142.225..362..587..959.1572..2587..4270
.0.13.13.14.15.20.27.41.58..91.145.240.398..680.1157.2003.3476..6073.10620
.0.21.21.22.23.29.38.58.81.127.203.341.574.1019.1784.3212.5779.10480.18971
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..760
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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)
k=3: a(n) = a(n-1) +a(n-2)
k=4: a(n) = 2*a(n-1) -a(n-3) for n>4
k=5: a(n) = 2*a(n-1) -a(n-3) for n>4
k=6: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-7) for n>8
k=7: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +2*a(n-4) -2*a(n-5) +a(n-6) -a(n-7) +a(n-8) -a(n-10) +a(n-11) for n>12
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .0..0..0..0
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CROSSREFS
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Column 2 is A000045(n-1).
Column 3 is A000045(n-1).
Column 4 is A001611(n-1).
Column 5 is A157725(n-1).
Sequence in context: A240753 A202149 A236533 * A298183 A098356 A298167
Adjacent sequences: A298184 A298185 A298186 * A298188 A298189 A298190
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Jan 14 2018
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STATUS
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approved
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