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A132357 a(n) = 3a(n-1) - a(n-3) + 3a(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) = 0.5*3^(n+1)+(1/6)*(-1)^n-(2/3)*cos(Pi*n/3). Or, a(n)=0.5*3^(n+1)+0.5*[ -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

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 A261547 A237853 * A262875 A219867 A295201

Adjacent sequences:  A132354 A132355 A132356 * A132358 A132359 A132360

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Nov 24 2007

EXTENSIONS

More terms from Charles R Greathouse IV, Oct 08 2016

STATUS

approved

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Last modified September 19 11:06 EDT 2019. Contains 327192 sequences. (Running on oeis4.)