A296984 - OEIS

A296984

Number of n X 2 0..1 arrays with each 1 adjacent to 3, 4 or 5 king-move neighboring 1s.

1, 2, 4, 7, 14, 33, 77, 185, 460, 1148, 2881, 7264, 18335, 46325, 117117, 296154, 749008, 1894495, 4792002, 12121373, 30661425, 77559617, 196191748, 496279912, 1255373969, 3175556284, 8032794347, 20319525273, 51399691053, 130019197698

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + a(n-2) + 3*a(n-3) - 4*a(n-4) - 2*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(1 + x + 2*x^2)*(1 - x - 2*x^2 - 2*x^3) / (1 - 2*x - x^2 - 3*x^3 + 4*x^4 + 2*x^5 + 4*x^6). - Colin Barker, Feb 25 2019

EXAMPLE

Some solutions for n=7:

..1..1. .0..0. .1..1. .0..0. .1..1. .1..1. .1..1. .0..0. .0..0. .1..1

..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .0..0. .1..1. .1..1

..1..0. .1..1. .1..1. .1..1. .0..0. .1..1. .0..0. .1..1. .1..1. .0..0

..1..1. .1..0. .1..1. .0..0. .0..0. .1..1. .1..1. .1..1. .1..0. .0..0

..1..1. .0..1. .0..1. .0..0. .0..0. .1..1. .1..1. .0..0. .1..0. .1..1

..1..1. .1..1. .1..1. .0..0. .0..0. .1..1. .0..0. .0..0. .1..1. .1..1

..1..1. .1..1. .1..1. .0..0. .0..0. .0..0. .0..0. .0..0. .1..1. .1..1

CROSSREFS

Column 2 of A296990.

Sequence in context: A325303 A356781 A113122 * A116584 A152477 A019998

Adjacent sequences: A296981 A296982 A296983 * A296985 A296986 A296987

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 22 2017

STATUS

approved