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A297519
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T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.
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13
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1, 2, 1, 3, 5, 1, 4, 17, 11, 1, 6, 33, 49, 24, 1, 9, 65, 128, 177, 55, 1, 13, 193, 363, 624, 727, 123, 1, 19, 529, 1408, 2610, 3383, 2445, 276, 1, 28, 1185, 5079, 15896, 19187, 16173, 8931, 621, 1, 41, 2737, 16104, 85843, 193087, 134123, 80436, 33841, 1395, 1, 60, 7169
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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.......4........6..........9...........13............19
.1....5.....17......33.......65........193..........529..........1185
.1...11.....49.....128......363.......1408.........5079.........16104
.1...24....177.....624.....2610......15896........85843........402072
.1...55....727....3383....19187.....193087......1671315......11283382
.1..123...2445...16173...134123....1995817.....25184119.....253060180
.1..276...8931...80436...956810...22251457....424461759....6257746155
.1..621..33841..406779..6834267..249462938...7287075949..156485261895
.1.1395.120079.2013490.48617437.2728125667.119542912709.3789277002360
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..241
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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-2) +2*a(n-3) -a(n-5)
k=3: a(n) = a(n-1) +2*a(n-2) +30*a(n-3) +6*a(n-5) -124*a(n-6) -8*a(n-8) +64*a(n-9)
k=4: [order 32]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3)
n=2: a(n) = a(n-1) +4*a(n-3) +12*a(n-4)
n=3: [order 12]
n=4: [order 31]
n=5: [order 87]
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EXAMPLE
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Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .1..0..0..0. .1..1..1..0. .0..0..0..1
..0..1..0..1. .0..0..0..0. .0..1..0..0. .0..0..1..0. .0..1..1..1
..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..1..0..1. .0..0..0..0
..1..0..1..0. .0..1..1..1. .0..1..0..0. .1..0..0..0. .0..1..1..0
..1..1..0..1. .0..0..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..1
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CROSSREFS
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Column 2 is A295091.
Row 1 is A000930(n+1).
Sequence in context: A337884 A337883 A202179 * A297749 A173588 A286942
Adjacent sequences: A297516 A297517 A297518 * A297520 A297521 A297522
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Dec 31 2017
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STATUS
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approved
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