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A297749
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 3 or 4 neighboring 1s.
13
1, 2, 1, 3, 5, 1, 4, 19, 11, 1, 6, 37, 66, 24, 1, 9, 71, 174, 230, 55, 1, 13, 237, 452, 852, 1142, 123, 1, 19, 715, 2223, 3780, 5396, 4344, 276, 1, 28, 1665, 9733, 28540, 34159, 29773, 16384, 621, 1, 41, 4007, 32213, 187564, 462187, 290114, 162828, 72571, 1395
OFFSET
1,2
COMMENTS
Table starts
.1....2......3.......4.........6...........9............13.............19
.1....5.....19......37........71.........237...........715...........1665
.1...11.....66.....174.......452........2223..........9733..........32213
.1...24....230.....852......3780.......28540........187564........1003470
.1...55...1142....5396.....34159......462187.......5298077.......43194128
.1..123...4344...29773....290114.....6379211.....116064732.....1513886975
.1..276..16384..162828...2561262....92963365....2703029494....57155337030
.1..621..72571..945314..22815719..1407868835...67944280878..2266768029479
.1.1395.287634.5347977.202611948.20923328285.1646896960337.88219789959795
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: [order 14]
k=4: [order 40]
k=5: [order 77]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3)
n=2: a(n) = 2*a(n-1) -a(n-2) +6*a(n-3) +8*a(n-4) -10*a(n-5) -12*a(n-6)
n=3: [order 19]
n=4: [order 52]
EXAMPLE
Some solutions for n=5 k=4
..1..1..1..0. .0..1..1..0. .0..1..1..0. .1..1..0..0. .0..1..1..1
..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..0. .0..1..0..1
..0..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..0..1
..1..1..0..0. .0..1..1..1. .1..0..1..0. .1..1..0..0. .0..0..1..1
..0..0..1..0. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..0..0
CROSSREFS
Column 2 is A295091.
Row 1 is A000930(n+1).
Sequence in context: A337883 A202179 A297519 * A173588 A286942 A125076
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 05 2018
STATUS
approved