A185742 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock trace equal to some horizontal or vertical neighbor 2 X 2 subblock trace.

0, 24, 40, 144, 344, 1000, 2688, 7528, 20648, 57040, 156920, 432648, 1192128, 3286216, 9056584, 24960464, 68789400, 189584296, 522495232, 1440006312, 3968670312, 10937688528, 30144344504, 83078054856, 228963805504

Offset

1,2

Comments

Column 1 of A185750.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) + 8*a(n-4).

Empirical g.f.: 8*x^2*(3 - 4*x + 6*x^2) / (1 - 3*x + x^2 + 2*x^3 - 8*x^4). - Colin Barker, Feb 28 2018

Example

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

Crossrefs

Cf. A185750.

Sequence in context: A357699 A328375 A141717 * A286876 A181702 A304890

Adjacent sequences: A185739 A185740 A185741 * A185743 A185744 A185745

Keyword

nonn

Author

R. H. Hardin, Feb 01 2011

Status

approved