A186455 Number of (n+1) X 3 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

21, 30, 51, 88, 128, 197, 292, 457, 688, 1058, 1589, 2424, 3651, 5552, 8376, 12709, 19192, 29085, 43952, 66562, 100629, 152332, 230359, 348632, 527296, 797909, 1206940, 1826193, 2762528, 4179698, 6322981, 9566352, 14472171, 21895248

Offset

1,1

Comments

Column 2 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>8.

Empirical g.f.: x*(21 - 12*x - 9*x^2 + 28*x^3 - 30*x^4 + 4*x^5 + 2*x^6 + 4*x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

Example

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

Crossrefs

Cf. A186462.

Sequence in context: A336357 A317772 A308339 * A318081 A276655 A187965

Adjacent sequences: A186452 A186453 A186454 * A186456 A186457 A186458

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved