A296646 Number of n X 3 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.

7, 29, 111, 468, 1985, 8126, 33933, 141664, 588156, 2449547, 10201129, 42445694, 176698722, 735575546, 3061694857, 12744724374, 53051527226, 220828964794, 919220181758, 3826333903711, 15927393968521, 66299068852883

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) + 18*a(n-3) - 12*a(n-4) - 42*a(n-5) - 17*a(n- 6) + 9*a(n-7) + 7*a(n-8) + 13*a(n-9) + 2*a(n-10).

Empirical g.f.: x*(7 + 15*x + 11*x^2 - 54*x^3 - 55*x^4 - 8*x^5 + 16*x^6 + 20*x^7 + 15*x^8 + 2*x^9) / (1 - 2*x - 6*x^2 - 18*x^3 + 12*x^4 + 42*x^5 + 17*x^6 - 9*x^7 - 7*x^8 - 13*x^9 - 2*x^10). - Colin Barker, Feb 24 2019

Example

Some solutions for n=7:
..1..0..1. .0..0..0. .0..0..1. .1..0..0. .0..0..1. .0..0..0. .0..0..1
..0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..0..0. .0..1..0. .0..0..1
..1..0..1. .0..0..0. .0..1..0. .1..0..0. .1..0..0. .0..0..0. .0..0..0
..1..0..0. .1..0..1. .0..0..1. .0..1..0. .1..0..0. .1..0..1. .0..1..0
..0..0..1. .1..0..0. .1..0..0. .1..1..0. .0..0..0. .0..0..0. .0..1..0
..1..0..0. .0..0..0. .0..1..1. .1..0..0. .1..0..0. .0..1..0. .0..0..0
..1..0..0. .0..1..1. .1..0..0. .1..0..0. .1..0..0. .1..0..0. .0..0..1

Crossrefs

Column 3 of A296651.

Sequence in context: A246038 A049349 A124828 * A037094 A118171 A072261

Adjacent sequences: A296643 A296644 A296645 * A296647 A296648 A296649

Keyword

nonn

Author

R. H. Hardin, Dec 17 2017

Status

approved