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A301498
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 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, 2, 2, 5, 8, 3, 5, 3, 8, 13, 6, 15, 15, 6, 13, 21, 6, 45, 83, 45, 6, 21, 34, 11, 156, 329, 329, 156, 11, 34, 55, 26, 479, 1576, 2803, 1576, 479, 26, 55, 89, 43, 1455, 7454, 21787, 21787, 7454, 1455, 43, 89, 144, 82, 4493, 35118, 164346, 268802, 164346
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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
..2..3....2......3.......6.........6..........11............26.............43
..3..2....5.....15......45.......156.........479..........1455...........4493
..5..3...15.....83.....329......1576........7454.........35118.........164664
..8..6...45....329....2803.....21787......164346.......1261122........9663349
.13..6..156...1576...21787....268802.....3243936......39741611......487928765
.21.11..479...7454..164346...3243936....62812639....1238986634....24457707005
.34.26.1455..35118.1261122..39741611..1238986634...39447933621..1251613605582
.55.43.4493.164664.9663349.487928765.24457707005.1251613605582.63780972381537
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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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) -2*a(n-6) +a(n-7)
k=3: [order 19] for n>23
k=4: [order 77] for n>81
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..0..1..1. .0..1..0..0. .0..1..0..0
..1..0..1..0. .1..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..0
..0..0..0..1. .1..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..0
..0..0..0..1. .0..0..0..1. .1..1..1..1. .1..1..0..0. .0..0..0..1
..0..0..0..0. .0..0..0..0. .1..1..1..0. .0..0..0..1. .1..1..0..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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