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A297802
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T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.
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12
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1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567
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OFFSET
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1,5
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COMMENTS
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Table starts
.1...1......1.......1.........1...........1.............1...............1
.1...2.....11......24........38.........105...........381............1067
.1...4.....37.....100.......293........1320..........6215...........24879
.1...7....108.....422......2195.......16006........115773..........738989
.1..14....533....2936.....23781......320168.......4340367........46828204
.1..31...2434...17899....231921.....5511367.....123361724......2122878239
.1..69..10287..104985...2174696....91376524....3420197908.....94927605755
.1.155..45968..645568..21427001..1587468720..102189481612...4611250894511
.1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943
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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),
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5),
k=3: [order 15],
k=4: [order 37],
k=5: [order 95].
Empirical for row n:
n=1: a(n) = a(n-1),
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),
n=3: [order 21],
n=4: [order 55].
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EXAMPLE
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Some solutions for n=5, k=4
..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..1..1..0
..0..1..1..0. .0..1..1..1. .0..0..1..1. .1..1..1..0. .0..1..1..1
..0..0..1..0. .0..0..1..1. .1..1..0..1. .0..0..0..1. .0..1..1..1
..1..1..0..0. .0..1..1..1. .0..1..1..1. .0..1..1..0. .1..1..0..0
..1..1..0..0. .0..0..1..0. .0..1..1..0. .1..1..0..0. .0..0..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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