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A297637 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 3 neighboring 1s. 13
2, 3, 4, 5, 8, 8, 8, 29, 20, 16, 13, 69, 113, 51, 32, 21, 200, 374, 494, 132, 64, 34, 552, 1657, 2370, 2344, 341, 128, 55, 1641, 6548, 17305, 16508, 10587, 883, 256, 89, 4685, 28645, 108928, 201152, 109790, 48187, 2293, 512, 144, 13716, 119531, 771393 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
...2....3.......5........8.........13...........21.............34
...4....8......29.......69........200..........552...........1641
...8...20.....113......374.......1657.........6548..........28645
..16...51.....494.....2370......17305.......108928.........771393
..32..132....2344....16508.....201152......2077060.......25139952
..64..341...10587...109790....2171757.....36084211......715726580
.128..883...48187...740555...24145671....659362756....21730243952
.256.2293..222804..5099557..273842684..12330890209...681285029028
.512.5964.1027173.35164860.3092881435.229556423760.21128576143262
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -3*a(n-2) -4*a(n-4) -a(n-5) +a(n-6)
k=3: [order 15]
k=4: [order 32]
k=5: [order 68]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) +6*a(n-4) -28*a(n-5) -24*a(n-6)
n=3: [order 18]
n=4: [order 40]
EXAMPLE
Some solutions for n=4 k=4
..1..0..1..0. .0..0..1..0. .1..0..0..1. .1..1..1..0. .1..1..0..0
..1..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0. .0..1..1..0
..1..0..1..0. .0..0..0..0. .0..1..0..0. .0..1..0..0. .1..1..0..0
..1..0..1..0. .0..0..0..1. .0..0..0..0. .1..1..1..0. .1..1..0..1
CROSSREFS
Column 1 is A000079.
Column 2 is A295346.
Row 1 is A000045(n+2).
Sequence in context: A297338 A297457 A297694 * A325415 A331076 A316496
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 02 2018
STATUS
approved

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Last modified July 13 08:08 EDT 2024. Contains 374274 sequences. (Running on oeis4.)