A298057 Number of n X 2 0..1 arrays with every element equal to 1, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 4, 3, 13, 32, 53, 125, 386, 727, 1601, 4568, 9985, 21185, 56082, 131531, 284005, 704432, 1701725, 3780885, 9013570, 21864175, 49853913, 116599048, 280872201, 652085433, 1515923218, 3617323651, 8484345565, 19735099744, 46724667589

Offset

1,2

Comments

Column 2 of A298063.

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 8*a(n-3) - 16*a(n-5).

Empirical g.f.: x*(1 + 3*x - 2*x^2 - 2*x^3 - 16*x^4) / (1 - x - x^2 - 8*x^3 + 16*x^5). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A298063.

Sequence in context: A105200 A088933 A019136 * A140884 A351992 A082383

Adjacent sequences: A298054 A298055 A298056 * A298058 A298059 A298060

Keyword

nonn

Author

R. H. Hardin, Jan 11 2018

Status

approved