A262415 Number of (n+1) X (3+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.

6, 45, 270, 1701, 10206, 61965, 371790, 2237301, 13423806, 80601885, 483611310, 2902199301, 17413195806, 104483957805, 626903746830, 3761465527701, 22568793166206, 135413146417725, 812478878506350, 4874876757822501

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 9*a(n-2) - 54*a(n-3).

Conjectures from Colin Barker, Dec 31 2018: (Start)

G.f.: 3*x*(2 + 3*x - 18*x^2) / ((1 - 3*x)*(1 + 3*x)*(1 - 6*x)).

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

a(n) = 3^(n-1) * (2^(n+3) - 4) / 2 for n odd.

(End)

Example

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

Crossrefs

Column 3 of A262420.

Sequence in context: A258350 A258623 A003486 * A297645 A201191 A214982

Adjacent sequences: A262412 A262413 A262414 * A262416 A262417 A262418

Keyword

nonn

Author

R. H. Hardin, Sep 22 2015

Status

approved