A186474 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

256, 205, 1098, 1251, 4895, 5955, 20079, 27101, 84228, 123227, 354915, 553287, 1501107, 2465976, 6374253, 10928793, 27157017, 48218637, 116026140, 211997451, 496891083, 929460999, 2132220387, 4065922560, 9164874045, 17754363633

Offset

1,1

Comments

Column 1 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>12.

Empirical g.f.: x*(256 - 307*x + 176*x^2 + 181*x^3 - 109*x^4 - 211*x^5 - 88*x^6 + 191*x^7 - 19*x^8 - 2*x^9 + 2*x^10 + 2*x^11) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - Colin Barker, Feb 28 2018

Example

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

Crossrefs

Cf. A186482.

Sequence in context: A103949 A057066 A186482 * A093861 A248776 A223600

Adjacent sequences: A186471 A186472 A186473 * A186475 A186476 A186477

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved