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A299521
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
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7
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 12, 2, 1, 1, 5, 5, 5, 5, 1, 1, 9, 33, 8, 33, 9, 1, 1, 22, 55, 41, 41, 55, 22, 1, 1, 45, 132, 117, 285, 117, 132, 45, 1, 1, 101, 272, 476, 1540, 1540, 476, 272, 101, 1, 1, 218, 630, 1743, 5869, 12411, 5869, 1743, 630, 218, 1, 1, 477, 1355, 7078
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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....2......5.......9........22.........45..........101...........218
.1...1..12....5.....33......55.......132........272..........630..........1355
.1...2...5....8.....41.....117.......476.......1743.........7078.........28743
.1...5..33...41....285....1540......5869......31464.......164344........875093
.1...9..55..117...1540...12411.....89125.....826509......7492106......69199615
.1..22.132..476...5869...89125....902141...12982595....174024827....2513147146
.1..45.272.1743..31464..826509..12982595..310347496...6868847887..161346598727
.1.101.630.7078.164344.7492106.174024827.6868847887.249358437986.9535286392860
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..197
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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) +3*a(n-2) -2*a(n-4) for n>5
k=3: [order 12] for n>13
k=4: [order 34] for n>36
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .0..0..1..1. .1..1..1..1. .0..0..1..1. .0..0..1..1
..1..1..1..0. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1
..1..1..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..1..1
..1..1..1..0. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..1..0
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CROSSREFS
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Column 2 is A052962(n-2).
Sequence in context: A211798 A075180 A227830 * A167164 A277265 A263631
Adjacent sequences: A299518 A299519 A299520 * A299522 A299523 A299524
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 11 2018
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STATUS
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approved
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