A186457 Number of (n+1) X 5 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

61, 88, 162, 309, 449, 673, 945, 1493, 2201, 3473, 5177, 7993, 11949, 18289, 27473, 41857, 63041, 95765, 144473, 219105, 330905, 501353, 757677, 1147281, 1734561, 2625569, 3970577, 6008917, 9088537, 13752497, 20802745, 31475673, 47614509

Offset

1,1

Comments

Column 4 of A186462.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>10.

Empirical g.f.: x*(61 - 34*x - 14*x^2 + 107*x^3 - 115*x^4 - 16*x^5 - 19*x^6 + 45*x^7 - 28*x^8 + 64*x^9) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

Example

Some solutions for 3 X 5:
..0..0..0..0..0....1..0..0..0..0....1..0..0..1..1....1..0..0..0..0
..0..0..0..0..0....0..1..0..0..0....0..0..0..0..1....1..0..0..0..0
..1..0..0..0..0....1..0..1..0..0....0..0..0..0..0....0..1..0..0..0

Crossrefs

Cf. A186462.

Sequence in context: A253232 A345239 A245759 * A103812 A047272 A123207

Adjacent sequences: A186454 A186455 A186456 * A186458 A186459 A186460

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved