A262326 Number of (n+1) X (2+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits.

3, 5, 15, 33, 99, 261, 783, 2241, 6723, 19845, 59535, 177633, 532899, 1595781, 4787343, 14353281, 43059843, 129153285, 387459855, 1162300833, 3486902499, 10460471301, 31381413903, 94143533121, 282430599363, 847289672325

Offset: 1

Author

R. H. Hardin, Sep 18 2015

Keywords

• nonn

Comments

Column 2 of A262332.

Examples

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

Links

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

Crossrefs

Cf. A262332.

Formula

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

Conjectures from Colin Barker, Mar 20 2018: (Start)

G.f.: x*(3 - 4*x - 9*x^2) / ((1 - 3*x)*(1 - 3*x^2)).

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

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

(End)