A186466 Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

277, 243, 942, 1203, 3190, 4023, 9982, 13985, 32390, 48553, 105436, 165842, 344498, 562526, 1130820, 1898670, 3724364, 6385226, 12298364, 21417538, 40692652, 71701562, 134848628, 239701634, 447381180, 800490426, 1485546884, 2671168754

Offset

1,1

Comments

Column 3 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>12.

Empirical g.f.: x*(277 - 311*x + 179*x^2 + 184*x^3 - 294*x^4 - 210*x^5 + 276*x^6 - 170*x^7 + 176*x^8 + 4*x^9 - 2*x^10 + x^11) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

Example

Some solutions for 3 X 4:
..1..0..1..0....0..0..0..0....1..2..0..1....0..0..0..0....1..0..0..0
..0..1..0..1....1..0..0..0....2..0..2..0....0..0..0..0....0..1..0..0
..2..0..1..2....0..1..0..0....0..2..0..2....1..0..0..2....1..0..1..1

Crossrefs

Cf. A186472.

Sequence in context: A169976 A297755 A166192 * A045022 A108253 A108255

Adjacent sequences: A186463 A186464 A186465 * A186467 A186468 A186469

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved