A297096 Number of n X 2 0..1 arrays with no 1 adjacent to 4 king-move neighboring 1s.

4, 16, 58, 216, 808, 3016, 11264, 42080, 157192, 587200, 2193552, 8194256, 30610528, 114348992, 427163264, 1595715392, 5960970560, 22267862080, 83184051328, 310743185408, 1160815393920, 4336353754624, 16198927050240, 60512876123648

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 6*a(n-3) - 8*a(n-4) - 4*a(n-6).

Empirical g.f.: 2*x*(2 + x^2 - 4*x^3 - 2*x^4 - 2*x^5) / (1 - 4*x + 2*x^2 - 6*x^3 + 8*x^4 + 4*x^6). - Colin Barker, Feb 26 2019

Example

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

Crossrefs

Column 2 of A297102.

Sequence in context: A134762 A207276 A047123 * A330791 A032094 A282083

Adjacent sequences: A297093 A297094 A297095 * A297097 A297098 A297099

Keyword

nonn

Author

R. H. Hardin, Dec 25 2017

Status

approved