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A300646
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 2, 4, 0, 0, 9, 10, 10, 9, 0, 0, 19, 30, 64, 30, 19, 0, 0, 41, 104, 316, 316, 104, 41, 0, 0, 88, 340, 1789, 2998, 1789, 340, 88, 0, 0, 189, 1144, 9738, 28089, 28089, 9738, 1144, 189, 0, 0, 406, 3795, 54293, 268615, 456649, 268615, 54293, 3795
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OFFSET
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1,8
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COMMENTS
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Table starts
.0...0....0......0........0..........0............0..............0
.0...1....2......4........9.........19...........41.............88
.0...2....2.....10.......30........104..........340...........1144
.0...4...10.....64......316.......1789.........9738..........54293
.0...9...30....316.....2998......28089.......268615........2552014
.0..19..104...1789....28089.....456649......7455411......121708555
.0..41..340...9738...268615....7455411....209156119.....5850560104
.0..88.1144..54293..2552014..121708555...5850560104...280782187131
.0.189.3795.300456.24338903.1990954802.164070075524.13506744672543
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..241
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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) +2*a(n-2) +a(n-3)
k=3: [order 15]
k=4: [order 49]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..1
..0..1..0..0. .0..1..0..0. .1..1..1..1. .1..1..0..0. .0..0..1..0
..1..1..0..0. .0..0..0..1. .1..0..1..1. .0..0..1..1. .1..1..0..0
..1..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..1..1. .1..0..0..0
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CROSSREFS
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Column 2 is A078039(n-2).
Sequence in context: A317643 A179011 A300465 * A300776 A301400 A134315
Adjacent sequences: A300643 A300644 A300645 * A300647 A300648 A300649
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 10 2018
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STATUS
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approved
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