A296335 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.

2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 47, 64, 47, 13, 21, 116, 230, 230, 116, 21, 34, 286, 816, 1235, 816, 286, 34, 55, 705, 2895, 6504, 6504, 2895, 705, 55, 89, 1738, 10277, 34224, 50595, 34224, 10277, 1738, 89, 144, 4285, 36480, 180404, 392230, 392230, 180404

Offset

1,1

Comments

Table starts

..2....3......5.......8........13.........21...........34............55

..3....8.....19......47.......116........286..........705..........1738

..5...19.....64.....230.......816.......2895........10277.........36480

..8...47....230....1235......6504......34224.......180404........950451

.13..116....816....6504.....50595.....392230......3051494......23717411

.21..286...2895...34224....392230....4476519.....51335713.....587914968

.34..705..10277..180404...3051494...51335713....869077778...14686634221

.55.1738..36480..950451..23717411..587914968..14686634221..366077961514

.89.4285.129486.5007796.184355308.6733523523.248214082895.9126072558650

Links

R. H. Hardin, Table of n, a(n) for n = 1..419

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +2*a(n-4) +a(n-5)

k=3: a(n) = 2*a(n-1) +4*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-9)

k=4: [order 21]

k=5: [order 44]

Example

Some solutions for n=5 k=4
..1..0..0..1. .0..0..1..0. .1..0..1..1. .0..0..1..1. .1..1..0..1
..0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..1..0. .1..0..0..0
..0..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..0
..1..0..0..0. .1..0..0..0. .0..1..0..1. .1..1..0..0. .1..0..0..0

Crossrefs

Column 1 is A000045(n+2).

Sequence in context: A053218 A198335 A339050 * A296635 A295051 A295379

Adjacent sequences: A296332 A296333 A296334 * A296336 A296337 A296338

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 10 2017

Status

approved