A186461 Number of (n+1) X 9 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

359, 457, 846, 1493, 2285, 3677, 5633, 9477, 13245, 20281, 27573, 43177, 62025, 98157, 144825, 224381, 333321, 511281, 765293, 1167881, 1755461, 2669577, 4022697, 6104941, 9213769, 13965837, 21097609, 31954865, 48300653, 73123993

Offset

1,1

Comments

Column 8 of A186462.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>14.

Empirical g.f.: x*(359 - 261*x - 68*x^2 + 519*x^3 - 505*x^4 + 244*x^5 + 30*x^6 + 641*x^7 - 1432*x^8 - 12*x^9 - 1624*x^10 + 1200*x^11 - 780*x^12 + 1936*x^13) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 18 2018

Example

Some solutions for 3 X 9:
..0..1..0..1..0..0..0..0..0....1..0..0..1..0..0..0..0..0
..0..0..1..0..1..0..0..0..0....0..0..0..0..1..0..0..0..0
..0..0..0..1..0..1..1..1..1....0..0..0..0..0..1..0..0..1

Crossrefs

Cf. A186462.

Sequence in context: A145533 A273806 A292618 * A344285 A344286 A142381

Adjacent sequences: A186458 A186459 A186460 * A186462 A186463 A186464

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved