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A299128
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 7 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, 9, 16, 8, 13, 50, 23, 23, 50, 13, 21, 112, 31, 232, 31, 112, 21, 34, 348, 184, 623, 623, 184, 348, 34, 55, 1028, 427, 3368, 2636, 3368, 427, 1028, 55, 89, 2796, 1115, 20226, 13809, 13809, 20226, 1115, 2796, 89, 144, 8216, 4128, 95305
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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....9.....23......31.......184.........427.........1115...........4128
..5...16...23....232.....623......3368.......20226........95305.........517446
..8...50...31....623....2636.....13809......132409.......854671........5933446
.13..112..184...3368...13809....198753.....2286535.....21688754......284403950
.21..348..427..20226..132409...2286535....50126162....761448901....14747885320
.34.1028.1115..95305..854671..21688754...761448901..17703574257...537784640291
.55.2796.4128.517446.5933446.284403950.14747885320.537784640291.28274774976231
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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=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..1
..0..1..1..0. .0..1..1..0. .0..0..1..1. .0..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0
..0..0..1..0. .0..1..0..0. .1..0..1..0. .1..0..1..1. .1..1..1..1
..1..0..0..1. .0..1..0..0. .1..0..1..0. .1..0..1..1. .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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