A186456 Number of (n+1) X 4 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

42, 51, 111, 162, 270, 362, 590, 846, 1362, 1998, 3122, 4622, 7126, 10642, 16286, 24442, 37230, 56046, 85138, 128414, 194754, 294094, 445590, 673362, 1019630, 1541514, 2333390, 3528654, 5340178, 8076974, 12221906, 18487374, 27972502

Offset

1,1

Comments

Column 3 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>9.

Empirical g.f.: x*(42 - 33*x + 9*x^2 + 24*x^3 - 36*x^4 - 16*x^5 + 19*x^6 - 7*x^7 + 16*x^8) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

Example

Some solutions for 3 X 4:
..1..0..0..0....1..1..0..1....0..0..0..0....0..0..0..1....1..0..0..1
..0..0..0..0....1..0..1..0....1..0..0..0....0..0..0..0....1..0..0..0
..0..0..0..0....0..1..0..1....1..1..0..0....1..0..0..0....1..0..0..0

Crossrefs

Cf. A186462.

Sequence in context: A249043 A063998 A255513 * A181647 A105346 A108119

Adjacent sequences: A186453 A186454 A186455 * A186457 A186458 A186459

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved