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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 02 2007
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 28 2008
STATUS
approved