A262267 Number of (n+2) X (1+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.

2, 4, 7, 13, 26, 52, 103, 205, 410, 820, 1639, 3277, 6554, 13108, 26215, 52429, 104858, 209716, 419431, 838861, 1677722, 3355444, 6710887, 13421773, 26843546, 53687092, 107374183, 214748365, 429496730, 858993460, 1717986919, 3435973837

Offset: 1

Author

R. H. Hardin, Sep 17 2015

Keywords

• nonn

Comments

Column 1 of A262274.

Examples

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

Links

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

Crossrefs

Cf. A262274.

Formula

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

Conjectures from Colin Barker, Feb 21 2018: (Start)

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

a(n) = 1/2 + 2^(2+n)/5 - (1/20-i/20)*((1+2*i)*(-i)^n + (2+i)*i^n) where i=sqrt(-1).

(End)