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

1,1

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).

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

Example

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

Crossrefs

Column 2 of A259222.

Sequence in context: A164434 A164494 A164407 * A339867 A135283 A225519

Adjacent sequences: A259213 A259214 A259215 * A259217 A259218 A259219

Keyword

nonn,easy

Author

R. H. Hardin, Jun 21 2015

Status

approved