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A304704
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 8, 10, 3, 5, 51, 21, 21, 51, 5, 8, 165, 46, 48, 46, 165, 8, 13, 306, 103, 215, 215, 103, 306, 13, 21, 993, 201, 798, 908, 798, 201, 993, 21, 34, 2867, 512, 3055, 5232, 5232, 3055, 512, 2867, 34, 55, 6818, 1123, 9810, 19701, 47440, 19701
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OFFSET
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1,5
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COMMENTS
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Table starts
..0....1....1.....2......3........5.........8..........13...........21
..1....3...11....10.....51......165.......306.........993.........2867
..1...11....8....21.....46......103.......201.........512.........1123
..2...10...21....48....215......798......3055........9810........41744
..3...51...46...215....908.....5232.....19701......135455.......872954
..5..165..103...798...5232....47440....296646.....2733069.....26024851
..8..306..201..3055..19701...296646...3510334....37931518....611105804
.13..993..512..9810.135455..2733069..37931518...799135415..19924071081
.21.2867.1123.41744.872954.26024851.611105804.19924071081.758781064050
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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) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6
k=3: [order 17] for n>20
k=4: [order 67] for n>69
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..0..1..0. .0..1..0..0. .0..1..1..0
..1..0..0..0. .0..1..1..0. .1..0..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..0. .1..1..1..1. .0..0..0..1. .1..0..0..0. .0..1..1..0
..1..0..0..1. .0..1..1..0. .1..0..0..1. .0..0..0..1. .0..1..1..0
..0..1..0..0. .0..1..1..1. .0..0..0..0. .0..1..0..0. .0..0..0..0
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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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