A296109 Number of n X 2 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.

1, 2, 3, 4, 8, 17, 31, 71, 166, 365, 856, 2020, 4675, 10985, 25869, 60578, 142347, 334748, 785984, 1846905, 4340975, 10198815, 23965446, 56319245, 132336896, 310971516, 730753851, 1717154937, 4035069173, 9481906914, 22281135563

Offset

1,2

Comments

Column 2 of A296115.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 5*a(n-3) - 2*a(n-4) - 6*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(1 + x - x^2 - 8*x^3 - 10*x^4 - 4*x^5) / (1 - x - 2*x^2 - 5*x^3 + 2*x^4 + 6*x^5 + 4*x^6). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A296115.

Sequence in context: A140974 A349763 A360000 * A102276 A215897 A276673

Adjacent sequences: A296106 A296107 A296108 * A296110 A296111 A296112

Keyword

nonn

Author

R. H. Hardin, Dec 04 2017

Status

approved