A296668 - OEIS

A296668

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

3, 10, 25, 68, 208, 609, 1785, 5375, 16174, 48589, 146652, 443220, 1339225, 4049457, 12250187, 37060306, 112130705, 339304900, 1026763976, 3107142321, 9402919993, 28455721175, 86115053750, 260609950693, 788686494268, 2386813930604

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

OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 3*a(n-1) + 5*a(n-3) - 10*a(n-4) - 12*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(3 + x - 5*x^2 - 22*x^3 - 16*x^4 - 4*x^5) / (1 - 3*x - 5*x^3 + 10*x^4 + 12*x^5 + 4*x^6). - Colin Barker, Feb 24 2019

EXAMPLE

Some solutions for n=7:

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

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

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

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

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

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

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

CROSSREFS

Column 2 of A296674.

Sequence in context: A026965 A130783 A026975 * A026985 A319919 A027227

Adjacent sequences: A296665 A296666 A296667 * A296669 A296670 A296671

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 18 2017

STATUS

approved