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A299307
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
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6
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0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 223, 223, 174, 5, 8, 604, 849, 1024, 849, 604, 8, 13, 2048, 3387, 5360, 5360, 3387, 2048, 13, 21, 6948, 13075, 28374, 55390, 28374, 13075, 6948, 21, 34, 23652, 51006, 144040, 482418, 482418, 144040, 51006
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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
..1.....4.....18......52.......174.........604.........2048...........6948
..1....18.....56.....223.......849........3387........13075..........51006
..2....52....223....1024......5360.......28374.......144040.........743640
..3...174....849....5360.....55390......482418......3860858.......34734150
..5...604...3387...28374....482418.....6525374.....76611604.....1041660250
..8..2048..13075..144040...3860858....76611604...1227812226....23819382545
.13..6948..51006..743640..34734150..1041660250..23819382545...723886147451
.21.23652.199243.3857242.308990628.14216373088.471369052777.22415064379413
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
k=3: [order 20] for n>21
k=4: [order 68] for n>70
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..0. .0..1..0..1. .0..1..1..1. .0..0..1..0
..1..0..1..0. .0..1..0..1. .0..1..1..0. .1..0..0..1. .1..1..0..1
..1..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..1..0. .1..1..1..1
..0..1..1..1. .0..1..0..1. .0..0..0..1. .1..0..0..1. .1..1..1..0
..0..1..1..1. .1..1..0..0. .0..1..1..1. .1..1..0..1. .0..0..1..0
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CROSSREFS
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Column 1 is A000045(n-1).
Column 2 is A297945.
Column 3 is A298384.
Sequence in context: A297951 A298560 A298389 * A298770 A299567 A299465
Adjacent sequences: A299304 A299305 A299306 * A299308 A299309 A299310
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Feb 06 2018
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STATUS
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approved
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