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A297457
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0 or 2 neighboring 1s.
13
2, 3, 4, 5, 8, 8, 8, 25, 19, 16, 13, 57, 92, 48, 32, 21, 156, 285, 390, 120, 64, 34, 384, 1143, 1677, 1652, 299, 128, 55, 1009, 3933, 10579, 9774, 6888, 747, 256, 89, 2545, 14817, 52714, 97005, 55713, 28971, 1865, 512, 144, 6580, 52868, 303202, 693884, 862112
OFFSET
1,1
COMMENTS
Table starts
...2....3......5........8........13..........21...........34.............55
...4....8.....25.......57.......156.........384.........1009...........2545
...8...19.....92......285......1143........3933........14817..........52868
..16...48....390.....1677.....10579.......52714.......303202........1595942
..32..120...1652.....9774.....97005......693884......6088511.......46944276
..64..299...6888....55713....862112.....8800153....116817805.....1310421193
.128..747..28971...321030...7800563...113851142...2300975096....37653648610
.256.1865.121854..1848151..70510494..1469935404..45221328552..1078420953679
.512.4656.512165.10625522.636242985.18934230754.886373249313.30786030956559
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4)
k=3: a(n) = 5*a(n-1) -3*a(n-2) +4*a(n-3) -25*a(n-4) +10*a(n-5) -7*a(n-6) +12*a(n-7)
k=4: [order 11]
k=5: [order 27]
k=6: [order 55]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) +a(n-3) +4*a(n-4)
n=3: a(n) = 3*a(n-1) +4*a(n-2) -7*a(n-3) +8*a(n-4) -19*a(n-5) +8*a(n-6) +2*a(n-8)
n=4: [order 15]
n=5: [order 33]
n=6: [order 72]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..0..0..0. .0..0..1..0. .1..0..0..0. .1..0..0..0
..0..0..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..0. .1..0..0..1
..0..0..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0
..0..0..0..1. .0..0..0..1. .0..0..1..1. .1..0..0..0. .0..0..1..0
..0..0..0..0. .0..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..1
CROSSREFS
Column 1 is A000079.
Column 2 is A295045.
Row 1 is A000045(n+2).
Sequence in context: A275465 A185198 A297338 * A297694 A297637 A325415
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 30 2017
STATUS
approved