A166152 a(n) = (6^n+12*(-7)^n)/13.

1, -6, 48, -300, 2316, -14916, 112188, -738660, 5450556, -36474276, 265397628, -1797317220, 12944017596, -88431340836, 632080079868, -4346196394980, 30893559749436, -213433808338596, 1510963317814908

Offset: 0

Author

Philippe Deléham, Oct 08 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, 42).

Crossrefs

Cf. A166035, A166036, A166149.

Programs

Mathematica

LinearRecurrence[{-1,42}, {1,-6}, 50] (* G. C. Greubel, May 01 2016 *)
Table[(6^n+12*(-7)^n)/13,{n,0,30}] (* Harvey P. Dale, Jun 01 2019 *)

PARI

a(n)=(6^n+12*(-7)^n)/13 \\ Charles R Greathouse IV, May 02 2016

Formula

a(n) = 42*a(n-2)-a(n-1), a(0)= 1, a(1)= -6, for n>1.

G.f.: (1-5x)/(1+x-42*x^2).

a(n)= Sum_{k, 0<=k<=n} A112555(n,k)*(-7)^k.

E.g.f.: (1/13)*(exp(6*x) + 12*exp(-7*x)). - G. C. Greubel, May 01 2016