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

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