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A318343
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 20, 20, 16, 32, 42, 36, 36, 42, 32, 64, 89, 76, 67, 76, 89, 64, 128, 190, 160, 148, 148, 160, 190, 128, 256, 407, 344, 343, 393, 343, 344, 407, 256, 512, 873, 748, 817, 1115, 1115, 817, 748, 873, 512, 1024, 1874, 1624, 1975, 3321
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OFFSET
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1,2
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COMMENTS
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Table starts
...1...2....4....8....16.....32......64......128.......256........512
...2...6...10...20....42.....89.....190......407.......873.......1874
...4..10...20...36....76....160.....344......748......1624.......3544
...8..20...36...67...148....343.....817.....1975......4788......11644
..16..42...76..148...393...1115....3321....10111.....30943......95244
..32..89..160..343..1115...4133...16267....66070....270320....1112195
..64.190..344..817..3321..16267...86487...476348...2647555...14797928
.128.407..748.1975.10111..66070..476348..3590263..27322989..209259065
.256.873.1624.4788.30943.270320.2647555.27322989.285034170.2994059337
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..611
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6
k=3: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) -2*a(n-4) +2*a(n-5) for n>6
k=4: [order 8] for n>9
k=5: [order 15] for n>18
k=6: [order 23] for n>27
k=7: [order 36] for n>41
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..0..0..0. .1..1..1..1
..1..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..0..0..0. .1..1..1..0. .1..1..1..0
..0..1..1..0. .1..0..0..1. .0..0..0..1. .1..1..0..0. .1..1..0..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A317759.
Sequence in context: A097089 A317764 A318075 * A318024 A320409 A096466
Adjacent sequences: A318340 A318341 A318342 * A318344 A318345 A318346
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Aug 24 2018
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STATUS
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approved
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