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A306172
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
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6
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1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 53, 30, 30, 53, 13, 21, 105, 66, 93, 66, 105, 21, 34, 237, 123, 249, 249, 123, 237, 34, 55, 577, 252, 544, 832, 544, 252, 577, 55, 89, 1205, 535, 1372, 1956, 1956, 1372, 535, 1205, 89, 144, 2681, 1074, 3411, 5421, 5277
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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
..2....5....9...21....53....105....237.....577.....1205.....2681......6349
..3....9...13...30....66....123....252.....535.....1074.....2194......4530
..5...21...30...93...249....544...1372....3411.....8269....20472.....50397
..8...53...66..249...832...1956...5421...15993....42682...118773....341634
.13..105..123..544..1956...5277..16195...52752...158458...503426...1626380
.21..237..252.1372..5421..16195..53834..185090...619073..2213741...7903854
.34..577..535.3411.15993..52752.185090..722779..2706166.10841923..44886700
.55.1205.1074.8269.42682.158458.619073.2706166.11592019.54162509.259464240
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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) +8*a(n-3) -4*a(n-4)
k=3: a(n) = a(n-1) +4*a(n-3) +2*a(n-5) -a(n-7) -2*a(n-9) -2*a(n-11) -a(n-12)
k=4: [order 40] for n>41
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..1. .0..1..1..1. .0..1..1..1. .0..1..1..1. .0..0..1..1
..1..1..1..1. .0..0..1..1. .1..1..1..1. .1..1..1..0. .1..0..1..0
..1..1..1..0. .1..1..1..1. .0..0..1..1. .1..1..1..1. .0..0..0..0
..1..1..1..1. .0..1..1..1. .0..1..1..1. .1..1..1..1. .0..0..1..1
..0..1..1..1. .0..0..1..1. .1..1..1..1. .0..1..1..0. .0..0..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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