A152733 a(n) + a(n+1) + a(n+2) = 3^n.

0, 0, 3, 6, 18, 57, 168, 504, 1515, 4542, 13626, 40881, 122640, 367920, 1103763, 3311286, 9933858, 29801577, 89404728, 268214184, 804642555, 2413927662, 7241782986, 21725348961, 65176046880, 195528140640, 586584421923, 1759753265766, 5279259797298

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2, 2, 3).

Formula

From R. J. Mathar, Dec 12 2008: (Start)

a(n) = 3*A077834(n-3).

G.f.: 3*x^3/((1-3*x)*(1+x+x^2)). (End)

a(n) = (1/13)*(3^n + 12*cos((2*n*Pi)/3) + 2*sqrt(3)*sin((2*n*Pi)/3)), n=1,2,... - Zak Seidov, Dec 12 2008

Example

0 + 0 + 3 = 3^1; 0 + 3 + 6 = 3^2; 3 + 6 + 18 = 3^3; ...

Mathematica

k0=k1=0; lst={k0, k1}; Do[kt=k1; k1=3^n-k1-k0; k0=kt; AppendTo[lst, k1], {n, 1, 5!}]; lst
Rest[CoefficientList[Series[3x^3/((1-3x)(1+x+x^2)), {x, 0, 30}], x]] (* Harvey P. Dale, Aug 31 2014 *)

Prog

(Magma) [n le 2 select 0 else 3^(n-2) -Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 31 2014
(PARI) x='x+O('x^30); concat([0, 0], Vec(3*x^3/((1-3*x)*(1+x+x^2)))) \\ G. C. Greubel, Sep 01 2018

Crossrefs

Cf. A152728, A152729, A152730, A152731, A152732, A152725, A152726, A000212.

Sequence in context: A089325 A110593 A049368 * A215455 A211894 A173109

Adjacent sequences: A152730 A152731 A152732 * A152734 A152735 A152736

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Status

approved