A259216 Number of (n+1) X (2+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

13, 23, 40, 71, 127, 230, 421, 779, 1456, 2747, 5227, 10022, 19345, 37559, 73288, 143615, 282439, 557126, 1101709, 2183123, 4333408, 8613683, 17141395, 34143686, 68062297, 135760415, 270931576, 540909719, 1080276751, 2158057382, 4312075957

Offset: 1

Author

R. H. Hardin, Jun 21 2015

Keywords

• nonn
• easy

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-2).

Crossrefs

Column 2 of A259222.

Formula

a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).

From Colin Barker, Dec 24 2018: (Start)

G.f.: x*(13 - 16*x - 16*x^2) / ((1 - 2*x)*(1 - x - x^2)).

a(n) = 2^(1+n) + (3*2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).

(End)

a(n) = 2^(n+1)+3*A000045(n+3). - R. J. Mathar, Oct 09 2020