A186475 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

205, 362, 701, 2049, 3442, 8223, 14492, 35081, 64280, 150785, 281928, 646756, 1233097, 2780008, 5384887, 11965960, 23479960, 51563275, 102260008, 222407905, 444938056, 960071644, 1934442193, 4147066744, 8404992631, 17923081288

Offset

1,1

Comments

Column 2 of A186482.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>13.

Empirical g.f.: x*(205 - 48*x - 433*x^2 + 1153*x^3 - 1116*x^4 - 110*x^5 + 336*x^6 + 112*x^7- 33*x^8 + 3*x^9 + x^10 + 2*x^12) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - Colin Barker, Apr 18 2018

Example

Some solutions for 5 X 3:
..2..0..2....2..1..0....0..0..3....1..2..0....3..1..0....0..2..1....0..3..0
..0..2..0....2..0..1....0..0..0....1..0..2....0..0..1....0..0..2....2..0..3
..1..0..2....0..2..0....0..0..0....0..1..0....0..0..0....0..0..0....0..2..0
..0..1..0....3..0..2....2..0..0....0..0..1....3..0..0....3..0..0....0..0..2
..0..0..1....0..3..0....0..2..2....0..0..1....2..3..0....0..3..1....0..0..0

Crossrefs

Cf. A186482.

Sequence in context: A116177 A191834 A042983 * A020170 A260471 A249703

Adjacent sequences: A186472 A186473 A186474 * A186476 A186477 A186478

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved