A297860 Number of n X 2 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.

0, 1, 2, 5, 10, 25, 54, 125, 282, 641, 1454, 3301, 7490, 17001, 38582, 87565, 198730, 451025, 1023614, 2323125, 5272402, 11965881, 27156934, 61633501, 139879130, 317460001, 720485262, 1635163525, 3711054050, 8422351625, 19114786774

Offset

1,3

Comments

Column 2 of A297866.

Links

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

Formula

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

Empirical g.f.: x^2*(1 + 2*x + 2*x^2) / ((1 + x)*(1 - x - 2*x^2 - 2*x^3)). - Colin Barker, Feb 21 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
..1..0. .0..0. .0..0. .1..0. .1..0. .1..0. .0..0. .0..0. .0..0. .0..0
..1..1. .1..1. .0..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1
..1..1. .1..1. .1..1. .0..0. .0..0. .1..0. .1..0. .1..1. .0..1. .1..0
..0..0. .0..0. .1..1. .0..1. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0
..0..1. .0..1. .0..1. .1..1. .1..1. .1..0. .0..1. .1..0. .1..1. .1..0
..1..1. .1..1. .0..0. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1

Crossrefs

Cf. A297866.

Sequence in context: A018356 A026383 A162963 * A002094 A212709 A264867

Adjacent sequences: A297857 A297858 A297859 * A297861 A297862 A297863

Keyword

nonn

Author

R. H. Hardin, Jan 07 2018

Status

approved