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A304133
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 31, 19, 19, 31, 13, 21, 49, 33, 44, 33, 49, 21, 34, 103, 53, 80, 80, 53, 103, 34, 55, 193, 89, 140, 176, 140, 89, 193, 55, 89, 327, 155, 244, 320, 320, 244, 155, 327, 89, 144, 641, 261, 436, 582, 651, 582, 436, 261, 641, 144
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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.....89....144.....233.....377
..2...5...7..17...31...49...103...193...327....641...1207....2129....4039
..3...7...9..19...33...53....89...155...261....439....749....1271....2149
..5..17..19..44...80..140...244...436...800...1444...2584....4630....8328
..8..31..33..80..176..320...582..1112..2178...4222...8066...15568...30220
.13..49..53.140..320..651..1321..2673..5293..10668..21704...43407...86685
.21.103..89.244..582.1321..2945..6333.13315..28932..63006..134021..284831
.34.193.155.436.1112.2673..6333.14708.33148..76987.180185..411855..940653
.55.327.261.800.2178.5293.13315.33148.79188.192201.476031.1166023.2823979
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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) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
k=3: a(n) = a(n-1) +2*a(n-3) for n>7
k=4: a(n) = a(n-1) +3*a(n-3) +a(n-5) -a(n-6) -5*a(n-7) -2*a(n-8) +2*a(n-10) for n>13
k=5: [order 16] for n>22
k=6: [order 45] for n>48
k=7: [order 79] for n>87
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..1..1..0. .0..0..1..1
..0..0..0..1. .0..0..0..1. .0..0..1..1. .1..1..1..1. .0..0..0..1
..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..1
..0..0..1..1. .0..0..0..0. .0..1..1..1. .1..1..1..0. .0..0..1..1
..0..0..0..1. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..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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