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A298230
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 5, 16, 8, 13, 50, 17, 17, 50, 13, 21, 112, 12, 195, 12, 112, 21, 34, 348, 100, 490, 490, 100, 348, 34, 55, 1028, 219, 2606, 1749, 2606, 219, 1028, 55, 89, 2796, 498, 15646, 7038, 7038, 15646, 498, 2796, 89, 144, 8216, 1999, 74688, 71212
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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....5.....17......12.......100........219..........498...........1999
..5...16...17....195.....490......2606......15646........74688.........397909
..8...50...12....490....1749......7038......71212.......440402........2785299
.13..112..100...2606....7038....110320....1166270.....10448313......136604409
.21..348..219..15646...71212...1166270...25406586....353699661.....6688607300
.34.1028..498..74688..440402..10448313..353699661...7311722995...215277571718
.55.2796.1999.397909.2785299.136604409.6688607300.215277571718.11308912804354
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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..1. .0..0..1..1. .0..1..0..1. .0..1..1..0. .0..1..0..0
..1..1..0..0. .0..0..1..1. .0..1..0..1. .0..1..1..0. .0..1..0..0
..0..1..0..0. .0..0..1..0. .1..1..0..0. .1..1..0..0. .1..1..1..0
..1..1..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0. .1..1..0..0
..1..1..0..0. .1..0..1..1. .0..0..0..1. .0..1..1..0. .0..1..0..0
..0..0..0..0. .1..0..1..1. .0..0..1..0. .0..1..1..0. .0..1..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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