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A132357 a(n)=3a(n-1)-a(n-3)+3a(n-4). +0
4
1, 4, 14, 41, 122, 364, 1093, 3280, 9842, 29525, 88574, 265720, 797161, 2391484 (list; graph; listen)
OFFSET

0,2

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 (mathar(AT)strw.leidenuniv.nl), 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 (richardchoulet(AT)yahoo.fr), 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 (ppl(AT)spl.at), Jun 09 2008

a(n+1)-3a(n) = A132367(n+1). - Paul Curtz (bpcrtz(AT)free.fr), Dec 02 2007

CROSSREFS

First differences of A132353.

Cf. A129339.

Sequence in context: A054443 A072674 A032285 this_sequence A124616 A124617 A124618

Adjacent sequences: A132354 A132355 A132356 this_sequence A132358 A132359 A132360

KEYWORD

nonn

AUTHOR

Paul Curtz (bpcrtz(AT)free.fr), Nov 24 2007

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Last modified December 3 01:16 EST 2008. Contains 151161 sequences.


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