A135266 Partial sums of A132357.

0, 1, 5, 19, 60, 182, 546, 1639, 4919, 14761, 44286, 132860, 398580, 1195741, 3587225, 10761679, 32285040, 96855122, 290565366, 871696099, 2615088299, 7845264901, 23535794706, 70607384120, 211822152360, 635466457081

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3,-1,4,-3).

Formula

a(n+1) - 3a(n) = 0, 1, 2, 4, 3, 2,... (periodically extended with period length 6) = partial sums of A132367.

a(n) = (1/4)*3^(n+1) - (1/12)*(-1)^n + (1/3)*cos(Pi*n/3) - (sqrt(3)/3)*sin (Pi*n/3) - 1. Or, a(n) = (1/4)*3^(n+1) + (1/4)*[ -3; -5; -7; -5; -3; -1] for n>=0. - Richard Choulet, Jan 02 2008

O.g.f.: x*(1 +x +2*x^2)/((3*x-1)*(x+1)(x^2-x+1)*(x-1)). - R. J. Mathar, Jul 28 2008

Mathematica

Join[{0}, Table[(1/4)*3^(n + 1) - (1/12)*(-1)^n + (1/3)*Cos[Pi*n/3] - (Sqrt[3]/3)*Sin [Pi*n/3] - 1, {n, 1, 25}] (* G. C. Greubel, Oct 07 2016 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -3, 4, -1, -3, 4]^n*[0; 1; 5; 19; 60])[1, 1] \\ Charles R Greathouse IV, Oct 08 2016

Crossrefs

Sequence in context: A092442 A341711 A328543 * A124123 A189714 A128638

Adjacent sequences: A135263 A135264 A135265 * A135267 A135268 A135269

Keyword

nonn,easy

Author

Paul Curtz, Dec 02 2007

Extensions

Edited and extended by R. J. Mathar, Jul 28 2008

Status

approved