A301361 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 3, 15, 13, 15, 3, 5, 37, 34, 34, 37, 5, 8, 90, 92, 101, 92, 90, 8, 13, 223, 256, 320, 320, 256, 223, 13, 21, 550, 721, 1167, 1356, 1167, 721, 550, 21, 34, 1355, 2036, 3961, 6279, 6279, 3961, 2036, 1355, 34, 55, 3341, 5701, 13974, 30236, 44148

Offset

1,5

Comments

Table starts

..0....1....1.....2......3........5.........8.........13...........21

..1....2....6....15.....37.......90.......223........550.........1355

..1....6...13....34.....92......256.......721.......2036.........5701

..2...15...34...101....320.....1167......3961......13974........49388

..3...37...92...320...1356.....6279.....30236.....147448.......713700

..5...90..256..1167...6279....44148....317019....2249565.....15884635

..8..223..721..3961..30236...317019...3241470...32453379....325518524

.13..550.2036.13974.147448..2249565..32453379..456790733...6500634810

.21.1355.5701.49388.713700.15884635.325518524.6500634810.132506438551

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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: [order 31]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A300344.

Sequence in context: A300435 A300769 A300639 * A267864 A336524 A219570

Adjacent sequences: A301358 A301359 A301360 * A301362 A301363 A301364

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 19 2018

Status

approved