A183775 Half the number of (n+1) X 3 binary arrays with no 2 X 2 subblock having exactly 2 ones.

4, 13, 47, 161, 567, 1969, 6887, 24001, 83799, 292305, 1020103, 3559137, 12419383, 43333873, 151206055, 527598593, 1840949015, 6423592977, 22413786247, 78208138529, 272890816759, 952194714417, 3322482302055, 11593099229761, 40451669182167, 141147546049105, 492504521037895

Offset

0,1

Links

R. H. Hardin, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (3,4,-8).

Formula

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

Empirical g.f.: (4 + x - 8*x^2) / (1 - 3*x - 4*x^2 + 8*x^3). - Colin Barker, Apr 04 2018

The above g.f. is correct. See A183782 for bounds on the order of the recurrence. - Andrew Howroyd, Jan 09 2025

Example

Some solutions with a(1,1)=0 for 5 X 3:
..0..1..0....0..1..1....0..0..0....0..1..0....0..1..0....0..0..0....0..0..0
..1..1..1....1..1..1....1..0..1....1..1..1....1..1..1....0..0..1....0..0..0
..1..0..1....1..1..1....0..0..0....1..1..1....1..0..1....0..1..1....1..0..0
..0..0..0....1..1..0....0..0..0....1..1..1....0..0..0....1..1..1....1..1..0
..0..0..0....1..1..1....0..1..0....1..1..1....1..0..0....1..1..0....1..1..1

Crossrefs

Column k=2 of A183782.

Sequence in context: A354550 A143566 A098841 * A363547 A017944 A017945

Adjacent sequences: A183772 A183773 A183774 * A183776 A183777 A183778

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 07 2011

Extensions

a(0) prepended by Andrew Howroyd, Jan 09 2025

Status

approved