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

Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4).

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)

The above empirical formula is correct. See note from Andrew Howroyd in A183986.

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: A183208 A048586 A080824 * A100602 A222175 A350767

Adjacent sequences: A183976 A183977 A183978 * A183980 A183981 A183982

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved