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A298154
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
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8
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1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 6, 16, 8, 13, 50, 18, 18, 50, 13, 21, 112, 15, 196, 15, 112, 21, 34, 348, 104, 497, 497, 104, 348, 34, 55, 1028, 227, 2618, 1822, 2618, 227, 1028, 55, 89, 2796, 510, 15694, 7250, 7250, 15694, 510, 2796, 89, 144, 8216, 2020, 74848, 72678
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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....4....4.....16......50.......112........348.........1028...........2796
..3....4....6.....18......15.......104........227..........510...........2020
..5...16...18....196.....497......2618......15694........74848.........398520
..8...50...15....497....1822......7250......72678.......448220........2829887
.13..112..104...2618....7250....111350....1177545.....10544116......137536697
.21..348..227..15694...72678...1177545...25625864....356815204.....6737133411
.34.1028..510..74848..448220..10544116..356815204...7382868491...216982050084
.55.2796.2020.398520.2829887.137536697.6737133411.216982050084.11381281119654
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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) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
k=3: [order 18] for n>19
k=4: [order 66] for n>68
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EXAMPLE
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Some solutions for n=6 k=4
..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..1
..1..1..0..1. .0..0..1..0. .1..0..1..1. .1..0..0..0. .1..1..0..0
..0..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0. .1..1..0..0
..1..1..0..1. .0..0..1..0. .0..0..0..1. .1..1..0..1. .1..1..0..1
..0..1..0..0. .1..1..1..1. .1..1..0..0. .1..0..0..0. .0..1..0..0
..0..1..0..0. .0..0..1..1. .1..1..0..0. .0..1..0..1. .1..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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