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A296327
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.
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7
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1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 11, 8, 1, 1, 15, 23, 23, 15, 1, 1, 26, 54, 61, 54, 26, 1, 1, 45, 122, 185, 185, 122, 45, 1, 1, 80, 278, 562, 853, 562, 278, 80, 1, 1, 140, 634, 1677, 3569, 3569, 1677, 634, 140, 1, 1, 245, 1438, 4998, 14691, 20088, 14691, 4998, 1438, 245, 1, 1
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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............1
.1...3....5.....8.....15......26.......45........80.........140..........245
.1...5...11....23.....54.....122......278.......634........1438.........3274
.1...8...23....61....185.....562.....1677......4998.......14968........44818
.1..15...54...185....853....3569....14691.....62193......261763......1099727
.1..26..122...562...3569...20088...112235....643541.....3666933.....20890748
.1..45..278..1677..14691..112235...850404...6660799....51754039....401363520
.1..80..634..4998..62193..643541..6660799..72224019...769931084...8196375877
.1.140.1438.14968.261763.3666933.51754039.769931084.11207386103.163095751500
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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) = a(n-1) +2*a(n-3) +a(n-5)
k=3: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -2*a(n-4) +4*a(n-5) -3*a(n-6) +2*a(n-7) -a(n-8)
k=4: [order 14]
k=5: [order 40]
k=6: [order 83]
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EXAMPLE
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Some solutions for n=5 k=4
..1..1..0..0. .1..1..0..1. .0..0..0..0. .0..1..1..0. .0..1..0..0
..1..0..0..0. .1..0..1..1. .0..0..0..0. .0..1..0..0. .1..1..0..0
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..0..0..1..1. .0..0..1..0. .0..1..0..1. .0..0..0..1. .1..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..1..0. .0..0..1..1. .1..0..1..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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