A186465 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

83, 129, 243, 562, 903, 1754, 2937, 5790, 9993, 19236, 33546, 63642, 112278, 210972, 375366, 700068, 1253442, 2324820, 4182330, 7725252, 13947186, 25682700, 46491258, 85412820, 154924338, 284132892, 516138474, 945381252, 1719241122

Offset

1,1

Comments

Column 2 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>11.

Empirical g.f.: x*(83 - 37*x - 98*x^2 + 279*x^3 - 280*x^4 + 8*x^5 + 60*x^6 + 12*x^7 + 4*x^8 - 2*x^9 + x^10) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

Example

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

Crossrefs

Cf. A186472.

Sequence in context: A261087 A140771 A142309 * A142409 A210527 A140038

Adjacent sequences: A186462 A186463 A186464 * A186466 A186467 A186468

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved