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A297519
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.
13
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
OFFSET
1,2
COMMENTS
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
LINKS
FORMULA
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]
EXAMPLE
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
CROSSREFS
Column 2 is A295091.
Row 1 is A000930(n+1).
Sequence in context: A337884 A337883 A202179 * A297749 A173588 A286942
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 31 2017
STATUS
approved