A297457 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0 or 2 neighboring 1s.

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

R. H. Hardin, Table of n, a(n) for n = 1..312

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

Adjacent sequences: A297454 A297455 A297456 * A297458 A297459 A297460

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2017

Status

approved