A296309 Number of n X 4 0..1 arrays with each 1 adjacent to 3 or 6 king-move neighboring 1s.

1, 4, 7, 10, 23, 45, 76, 150, 293, 532, 1010, 1942, 3625, 6833, 13005, 24499, 46186, 87489, 165230, 311809, 589569, 1114002, 2103636, 3975125, 7511104, 14188028, 26805754, 50647041, 95680777, 180765515, 341525717, 645225728, 1218995503

Offset

1,2

Links

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

Formula

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

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

Example

Some solutions for n=5:
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..1..1
..0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..1. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..0

Crossrefs

Column 4 of A296313.

Sequence in context: A275176 A024726 A024948 * A376884 A182278 A032818

Adjacent sequences: A296306 A296307 A296308 * A296310 A296311 A296312

Keyword

nonn

Author

R. H. Hardin, Dec 10 2017

Status

approved