A188700 Number of n X 3 binary arrays without the pattern 0 0 diagonally or vertically.

8, 21, 90, 304, 1141, 4084, 14925, 54049, 196508, 713225, 2590574, 9406448, 34159833, 124045128, 450458681, 1635781681, 5940155616, 21570956189, 78332387394, 284454730240, 1032963629229, 3751084683708, 13621618755397

Offset

1,1

Comments

Column 3 of A188706.

Links

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

Formula

Empirical: a(n) = a(n-1) + 8*a(n-2) + 6*a(n-3) - a(n-4) - a(n-5).

Empirical g.f.: x*(8 + 13*x + 5*x^2 - 2*x^3 - x^4) / ((1 + x)*(1 - 2*x - 6*x^2 + x^4)). - Colin Barker, Apr 28 2018

Example

Some solutions for 4 X 3:
..1..1..1....0..0..1....1..1..0....1..1..1....0..1..1....0..0..0....1..1..1
..1..0..1....1..1..1....1..1..1....0..1..1....1..1..0....1..1..1....0..1..0
..1..1..1....1..1..1....0..0..1....1..1..1....1..1..1....0..1..1....1..1..1
..1..0..1....1..1..0....1..1..1....0..1..1....1..0..0....1..1..1....0..1..1

Crossrefs

Cf. A188706.

Sequence in context: A226313 A275185 A264238 * A054855 A220611 A297340

Adjacent sequences: A188697 A188698 A188699 * A188701 A188702 A188703

Keyword

nonn

Author

R. H. Hardin, Apr 08 2011

Status

approved