login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132357 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4). 3
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

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).

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) = -(1/3)*(1/2 - (1/2)*i*sqrt(3))^n + (3/2)*3^n + (1/6)*(-1)^n - (1/3)*(1/2 + (1/2)*i*sqrt(3))^n, with n>=0 and i=sqrt(-1). - Paolo P. Lava, Jun 09 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

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

Adjacent sequences: A132354 A132355 A132356 * A132358 A132359 A132360

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 December 2 12:34 EST 2022. Contains 358496 sequences. (Running on oeis4.)