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A317733
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
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7
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0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 161, 98, 3, 5, 383, 1250, 1250, 383, 5, 8, 1493, 9541, 19208, 9541, 1493, 8, 13, 5824, 72715, 293378, 293378, 72715, 5824, 13, 21, 22717, 554642, 4458098, 8931649, 4458098, 554642, 22717, 21, 34, 88609, 4229957
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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
..1.....7.......25..........98...........383.............1493
..1....25......161........1250..........9541............72715
..2....98.....1250.......19208........293378..........4458098
..3...383.....9541......293378.......8931649........270714329
..5..1493....72715.....4458098.....270714329......16360102553
..8..5824...554642....67837952....8216055128.....990049380944
.13.22717..4229957..1032124178..249314217853...59904290609773
.21.88609.32260015.15703109762.7565327218559.3624564255839937
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..364
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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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)
k=3: a(n) = 6*a(n-1) +11*a(n-2) +11*a(n-3) -2*a(n-4) -a(n-5) -2*a(n-6)
k=4: a(n) = 12*a(n-1) +42*a(n-2) +107*a(n-3) -30*a(n-4) +12*a(n-5) -16*a(n-6)
k=5: [order 21]
k=6: [order 36]
k=7: [order 81]
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..0
..1..0..1..0. .1..1..0..0. .1..1..1..1. .1..1..0..0. .0..1..1..1
..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..1..0..1..1. .1..0..0..1. .1..0..0..1. .0..1..1..0. .1..0..0..0
..1..1..0..1. .1..0..1..1. .1..0..0..0. .0..1..1..0. .0..1..0..1
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CROSSREFS
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Column 1 is A000045(n-1).
Column 2 is A304421.
Sequence in context: A305692 A317072 A316953 * A258335 A266985 A286912
Adjacent sequences: A317730 A317731 A317732 * A317734 A317735 A317736
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Aug 05 2018
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STATUS
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approved
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