A166035 a(n) = (3^n+6*(-4)^n)/7.

1, -3, 15, -51, 231, -843, 3615, -13731, 57111, -221883, 907215, -3569811, 14456391, -57294123, 230770815, -918300291, 3687550071, -14707153563, 58957754415, -235443597171, 942936650151, -3768259816203, 15083499618015

Offset: 0

Author

Philippe Deléham, Oct 05 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,12).

Crossrefs

Cf. A077925, A091004.

Programs

Mathematica

LinearRecurrence[{-1, 12}, {1, -3}, 100] (* G. C. Greubel, Apr 24 2016 *)

PARI

a(n)= (3^n+6*(-4)^n)/7;
for(n=0,33,print1(a(n),", "));

Formula

a(n) = -a(n-1) + 12*a(n-2), a(0) = 1, a(1) = -3, for n>1.

a(n) = Sum_{0<=k<=n} A112555(n,k)*(-4)^k.

G.f.: (1-2x)/(1+x-12x^2).

E.g.f.: (1/7)*(exp(3*x) + 6*exp(-4*x)). - G. C. Greubel, Apr 24 2016

Extensions

a(5) corrected by Tilman Neumann, Dec 31 2010