A297917 Number of n X 2 0..1 arrays with every element equal to 1, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

1, 4, 17, 61, 216, 793, 2907, 10622, 38809, 141849, 518472, 1894989, 6926071, 25314486, 92523373, 338168845, 1235992136, 4517496689, 16511251075, 60347893838, 220568887889, 806169548561, 2946514113224, 10769379015141

Offset

1,2

Comments

Column 2 of A297923.

Links

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

Formula

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

Empirical g.f.: x*(1 + x + 4*x^2 + 2*x^3 - 4*x^4) / (1 - 3*x - x^2 - 4*x^3 - 4*x^4). - Colin Barker, Feb 19 2018

Example

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

Crossrefs

Cf. A297923.

Sequence in context: A034331 A107278 A006762 * A202752 A286210 A339286

Adjacent sequences: A297914 A297915 A297916 * A297918 A297919 A297920

Keyword

nonn

Author

R. H. Hardin, Jan 08 2018

Status

approved