A135344 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), with initial values 1,1,1,1.

1, 1, 1, 1, 5, 17, 53, 157, 469, 1405, 4217, 12653, 37961, 113881, 341641, 1024921, 3074765, 9224297, 27672893, 83018677, 249056029, 747168085, 2241504257, 6724512773, 20173538321, 60520614961, 181561844881, 544685534641, 1634056603925, 4902169811777

Offset: 0

Author

Paul Curtz, Dec 06 2007

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3, 0, -1, 3).

Crossrefs

Cf. A007395.

Programs

Mathematica

LinearRecurrence[{3,0,-1,3},{1,1,1,1},40] (* Harvey P. Dale, Apr 15 2012 *)

Formula

3*a(n) - a(n+1) = hexaperiodic 2, 2, 2, -2, -2, -2 = 2*A130151.

From Richard Choulet, Jan 02 2008: (Start)

a(n) = (1/14)*3^n + (1/6)*(-1)^n + (16/21)*cos(Pi*n/3) + (8*sqrt(3)/21)*sin(Pi*n/3).

a(n) = (1/14)*3^n + (1/14)*[13; 11; 5; -13; -11; -5]. (End)

G.f.: ( -1+2*x+2*x^2+x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - Harvey P. Dale, Apr 15 2012

42*a(n) = 7*(-1)^n +8*A167380(n+3) +3^(n+1). - R. J. Mathar, Oct 03 2021