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A305489
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 6 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, 14, 14, 2, 3, 33, 19, 33, 3, 5, 70, 27, 27, 70, 5, 8, 157, 137, 65, 137, 157, 8, 13, 346, 295, 195, 195, 295, 346, 13, 21, 769, 570, 125, 2094, 125, 570, 769, 21, 34, 1710, 2026, 268, 7007, 7007, 268, 2026, 1710, 34, 55, 3813, 4727, 1176, 16464, 23229
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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.........21..........34
..1....7...14...33.....70.....157.....346.......769.......1710........3813
..1...14...19...27....137.....295.....570......2026.......4727.......10623
..2...33...27...65....195.....125.....268......1176........805........1681
..3...70..137..195...2094....7007...16464.....91350.....348956.....1047508
..5..157..295..125...7007...23229...52124....581383....2463954.....8570618
..8..346..570..268..16464...52124...65452...2034173....7974852....20131094
.13..769.2026.1176..91350..581383.2034173..35294211..261130745..1568168588
.21.1710.4727..805.348956.2463954.7974852.261130745.2468446765.16736271764
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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) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
k=3: [order 14] for n>16
k=4: [order 17] for n>22
k=5: [order 97] for n>100
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..0..1..0. .0..0..1..0
..1..0..0..1. .0..1..1..0. .0..0..1..0. .0..1..1..1. .1..0..1..1
..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
..1..0..1..1. .0..0..1..0. .0..1..0..0. .1..1..1..0. .1..1..0..1
..1..0..0..1. .1..0..1..1. .0..1..1..0. .0..1..0..0. .1..0..0..1
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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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