A183804 1/16 the number of (n+1) X 3 binary arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

3, 13, 55, 237, 1011, 4341, 18567, 79605, 340803, 1460349, 6254199, 26793693, 114763635, 491621157, 2105830791, 9020628261, 38640044547, 165518326125, 709005955383, 3037082133069, 13009525105779, 55727225184213

Offset

1,1

Comments

Column 2 of A183811.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 9*a(n-2) - 15*a(n-3).

Empirical g.f.: x*(3 + 4*x - 11*x^2) / (1 - 3*x - 9*x^2 + 15*x^3). - Colin Barker, Apr 04 2018

Example

Some solutions with upper left block zero for 5 X 3:
  0 0 0    0 0 0    0 0 0    0 0 1    0 0 1    0 0 1    0 0 1
  0 0 1    0 0 1    0 0 1    0 0 1    0 0 1    0 0 0    0 0 1
  0 1 1    1 1 1    1 1 1    1 1 0    1 1 0    1 0 0    0 1 0
  0 1 1    1 1 0    1 0 0    1 0 0    1 1 1    0 1 1    1 1 0
  1 1 0    0 1 0    0 0 1    0 0 1    0 0 1    0 1 0    1 1 1

Crossrefs

Cf. A183811.

Sequence in context: A286191 A033887 A291653 * A117376 A264037 A151318

Adjacent sequences: A183801 A183802 A183803 * A183805 A183806 A183807

Keyword

nonn

Author

R. H. Hardin, Jan 07 2011

Status

approved