A304058 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 10, 6, 10, 3, 5, 51, 18, 18, 51, 5, 8, 165, 32, 26, 32, 165, 8, 13, 306, 60, 155, 155, 60, 306, 13, 21, 993, 124, 427, 596, 427, 124, 993, 21, 34, 2867, 288, 1122, 1641, 1641, 1122, 288, 2867, 34, 55, 6818, 598, 4109, 5415, 3434, 5415

Offset

1,5

Comments

Table starts

..0....1...1.....2......3......5.......8.......13........21.........34

..1....3..11....10.....51....165.....306......993......2867.......6818

..1...11...6....18.....32.....60.....124......288.......598.......1266

..2...10..18....26....155....427....1122.....4109.....13836......42480

..3...51..32...155....596...1641....5415....30207....124598.....500772

..5..165..60...427...1641...3434...13624....69126....260517....1102813

..8..306.124..1122...5415..13624...77360...478889...2630794...17166221

.13..993.288..4109..30207..69126..478889..4890117..30295907..239161610

.21.2867.598.13836.124598.260517.2630794.30295907.181435839.1835718615

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 15] for n>18

k=4: [order 57] for n>60

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A116854 A331692 A016567 * A305452 A304704 A316455

Adjacent sequences: A304055 A304056 A304057 * A304059 A304060 A304061

Keyword

nonn,tabl

Author

R. H. Hardin, May 05 2018

Status

approved