A297972 Number of n X 2 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

0, 1, 3, 6, 17, 41, 104, 261, 655, 1646, 4133, 10381, 26072, 65481, 164459, 413046, 1037385, 2605441, 6543688, 16434781, 41276727, 103668446, 260368189, 653926981, 1642368440, 4124885761, 10359845043, 26019239206, 65348545857, 164125953561

Offset

1,3

Comments

Column 2 of A297978.

Links

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

Formula

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

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

Example

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

Crossrefs

Cf. A297978.

Sequence in context: A151503 A319789 A007718 * A275057 A320807 A089264

Adjacent sequences: A297969 A297970 A297971 * A297973 A297974 A297975

Keyword

nonn

Author

R. H. Hardin, Jan 10 2018

Status

approved