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A135266 Partial sums of A132357. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A107179 A092442 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

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)