A228797 Number of 2 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.

2, 2, 8, 16, 42, 98, 240, 576, 1394, 3362, 8120, 19600, 47322, 114242, 275808, 665856, 1607522, 3880898, 9369320, 22619536, 54608394, 131836322, 318281040, 768398400, 1855077842, 4478554082, 10812186008, 26102926096, 63018038202, 152139002498

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Conjectures from Colin Barker, Sep 13 2018: (Start)

G.f.: 2*x / ((1 + x)*(1 - 2*x - x^2)).

a(n) = (-2*(-1)^n + (1-sqrt(2))^n + (1+sqrt(2))^n) / 2.

(End)

Example

Some solutions for n=4:
..1..0..0..1....1..0..0..1....1..0..0..0....1..0..0..1....1..0..0..1
..0..0..0..0....0..0..1..0....0..0..0..1....1..0..1..0....0..0..0..1

Crossrefs

Row 2 of A228796.

Sequence in context: A220172 A276054 A192305 * A052970 A220589 A109190

Adjacent sequences: A228794 A228795 A228796 * A228798 A228799 A228800

Keyword

nonn

Author

R. H. Hardin, Sep 04 2013

Status

approved