A186464 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

81, 83, 277, 367, 966, 1321, 3078, 4553, 10028, 15650, 32786, 53166, 107524, 179614, 353932, 604474, 1168188, 2028530, 3863852, 6793514, 12800564, 22716978, 42458812, 75878698, 140963524, 253237282, 468324588, 844629530, 1556731220

Offset

1,1

Comments

Column 1 of A186472.

Links

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

Formula

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

Empirical g.f.: x*(81 - 79*x + 30*x^2 + 54*x^3 - 37*x^4 - 40*x^5 - 4*x^6 + 26*x^7 - 2*x^8 + x^9) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Feb 28 2018

Example

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

Crossrefs

Cf. A186472.

Sequence in context: A186472 A183984 A089784 * A345477 A295700 A286898

Adjacent sequences: A186461 A186462 A186463 * A186465 A186466 A186467

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved