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

Author

R. H. Hardin, Sep 22 2015

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 3 of A262420.

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)