A186467 Number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

367, 562, 1203, 3186, 4875, 9834, 14883, 31866, 51057, 105398, 174289, 347428, 588058, 1145866, 1976438, 3787644, 6625638, 12540516, 22170114, 41575892, 74087098, 137980420, 247343794, 458282956, 825184634, 1523024532, 2751516210

Offset

1,1

Comments

Column 4 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>13.

Empirical g.f.: x*(367 - 172*x - 288*x^2 + 1686*x^3 - 1920*x^4 + 196*x^5 - 604*x^6 + 1428*x^7 - 1350*x^8 + 1364*x^9 + 36*x^10 - 18*x^11 + 9*x^12) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

Example

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

Crossrefs

Cf. A186472.

Sequence in context: A320711 A142236 A307009 * A054827 A059230 A212378

Adjacent sequences: A186464 A186465 A186466 * A186468 A186469 A186470

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved