The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132357 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4). 4
1, 4, 14, 41, 122, 364, 1093, 3280, 9842, 29525, 88574, 265720, 797161, 2391484, 7174454, 21523361, 64570082, 193710244, 581130733, 1743392200, 5230176602, 15690529805, 47071589414, 141214768240, 423644304721 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
O.g.f.: -(1+x+2*x^2)/((3*x-1)*(x+1)*(x^2-x+1)) = -(3/2)/(3*x-1)+(1/3)*(x-2)/(x^2-x+1)+(1/ 6)/(x+1). - R. J. Mathar, Nov 28 2007
a(n) = (1/2)*3^(n+1) + (1/6)*(-1)^n - (2/3)*cos(Pi*n/3). Or, a(n) = (1/2)*3^(n+1) + (1/2)*[ -1; -1; 1; 1; 1; -1]. - Richard Choulet, Jan 02 2008
a(n+1) - 3a(n) = A132367(n+1). - Paul Curtz, Dec 02 2007
6*a(n) = (-1)^n +3^(n+2) -2*A057079(n+1). - R. J. Mathar, Oct 03 2021
MATHEMATICA
LinearRecurrence[{3, 0, -1, 3}, {1, 4, 14, 41}, 50] (* Paolo Xausa, Dec 05 2023 *)
PROG
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 3, -1, 0, 3]^n*[1; 4; 14; 41])[1, 1] \\ Charles R Greathouse IV, Oct 08 2016
CROSSREFS
First differences of A132353.
Cf. A129339.
Sequence in context: A196713 A358587 A237853 * A262875 A219867 A295201
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 24 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 25 07:15 EDT 2024. Contains 372782 sequences. (Running on oeis4.)