A186458 Number of (n+1) X 6 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

106, 128, 270, 449, 797, 1061, 1681, 2285, 3681, 5281, 8437, 12401, 19317, 28641, 44073, 65877, 100705, 151229, 230209, 346689, 526453, 794241, 1204293, 1818849, 2755433, 4164309, 6305265, 9533069, 14429537, 21821729, 33023541, 49948881

Offset

1,1

Comments

Column 5 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>11.

Empirical g.f.: x*(106 - 84*x + 14*x^2 + 121*x^3 - 57*x^4 - 143*x^5 + 45*x^6 - 111*x^7 + 88*x^8 - 44*x^9 + 144*x^10) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

Example

Some solutions for 3 X 6:
..1..1..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..0....0..0..1..0..1..0
..0..0..1..0..0..0....0..0..0..0..0..1....1..0..0..0..0..0....0..0..0..1..0..1
..0..0..0..1..1..1....0..0..0..0..0..0....1..1..0..0..0..1....0..0..0..0..1..0

Crossrefs

Cf. A186462.

Sequence in context: A235691 A095645 A039554 * A158013 A250643 A163625

Adjacent sequences: A186455 A186456 A186457 * A186459 A186460 A186461

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved