A165758 a(n) = (12-7*6^n)/5.

1, -6, -48, -300, -1812, -10884, -65316, -391908, -2351460, -14108772, -84652644, -507915876, -3047495268, -18284971620, -109709829732, -658258978404, -3949553870436, -23697323222628, -142183939335780, -853103636014692

Offset: 0

Author

Philippe Deléham, Sep 26 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (7, -6).

Programs

Mathematica

(12-7*6^Range[0,20])/5 (* or *) LinearRecurrence[{7,-6},{1,-6},20] (* Harvey P. Dale, Apr 30 2012 *)

Formula

a(n) = 6*a(n-1) - 12, a(0)=1.

a(n) = 7*a(n-1)-6*a(n-2), a(0)=1, a(1)= -6.

G.f.: (1-13x)/(1-7x+6x^2).

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

a(n) = (-6)*A061801(n-1).

E.g.f.: (1/5)*(12*exp(x) - 7*exp(6*x)). - G. C. Greubel, Apr 07 2016

Extensions

Corrected by D. S. McNeil, Aug 20 2010