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A318350
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 7, 6, 7, 8, 13, 11, 13, 13, 11, 13, 21, 18, 21, 14, 21, 18, 21, 34, 30, 41, 29, 29, 41, 30, 34, 55, 49, 71, 55, 62, 55, 71, 49, 55, 89, 81, 130, 106, 136, 136, 106, 130, 81, 89, 144, 134, 237, 220, 279, 345, 279, 220, 237, 134, 144, 233, 221, 439
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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
..2..3...4...7...11...18....30.....49.....81.....134.....221......365.......603
..3..4...6..13...21...41....71....130....237.....439.....802.....1483......2734
..5..7..13..14...29...55...106....220....432.....885....1788.....3642......7416
..8.11..21..29...62..136...279....624...1344....2941....6444....14202.....31437
.13.18..41..55..136..345...842...2167...5544...14244...36572....94381....243153
.21.30..71.106..279..842..2429...7451..22996...70762..218768...677035...2090867
.34.49.130.220..624.2167..7451..27666.102454..375150.1393359..5163458..19078931
.55.81.237.432.1344.5544.22996.102454.463096.2057916.9235301.41554051.186399590
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LINKS
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FORMULA
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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) -a(n-6)
k=3: [order 19] for n>25
k=4: [order 37] for n>45
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..1..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..0. .1..0..1..0
..0..0..0..0. .0..0..0..0. .0..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..1..0. .0..1..1..0
..0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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