A183979 1/4 the number of (n+1) X 3 binary arrays with all 2 X 2 subblock sums the same.

6, 8, 11, 17, 27, 47, 83, 155, 291, 563, 1091, 2147, 4227, 8387, 16643, 33155, 66051, 131843, 263171, 525827, 1050627, 2100227, 4198403, 8394755, 16785411, 33566723, 67125251, 134242307, 268468227, 536920067, 1073807363, 2147581955, 4295098371

Offset

1,1

Comments

Column 2 of A183986.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 07 2018: (Start)

G.f.: x*(6 - 10*x - 13*x^2 + 20*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = (3*2^(n/2) + 2^n + 6) / 2 for n even.

a(n) = 2^(n-1) + 2^((n+1)/2) + 3 for n odd.

(End)

Example

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

Crossrefs

Cf. A183986.

Sequence in context: A048586 A080824 A100602 * A222175 A350767 A315856

Adjacent sequences: A183976 A183977 A183978 * A183980 A183981 A183982

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved