A299523 Number of n X 3 0..1 arrays with every element equal to 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 4, 1, 12, 35, 60, 269, 873, 1985, 7571, 24138, 65389, 225530, 714174, 2097771, 6892581, 21742964, 66279272, 212788613, 670024373, 2077242857, 6596234246, 20753371856, 64838337595, 204829582459, 644229872136, 2019822965143

Offset

1,2

Comments

Column 3 of A299528.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +18*a(n-3) -36*a(n-4) -45*a(n-5) -51*a(n-6) +111*a(n-7) +88*a(n-8) +94*a(n-9) +61*a(n-10) -89*a(n-11) -143*a(n-12) -109*a(n-13) +52*a(n-14) +11*a(n-15) -7*a(n-16) +3*a(n-17) for n>18.

Example

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

Crossrefs

Cf. A299528.

Sequence in context: A019236 A019237 A019238 * A157404 A135704 A373394

Adjacent sequences: A299520 A299521 A299522 * A299524 A299525 A299526

Keyword

nonn

Author

R. H. Hardin, Feb 11 2018

Status

approved