A166149 a(n) = (5^n + 10*(-6)^n)/11.

1, -5, 35, -185, 1235, -6785, 43835, -247385, 1562435, -8983985, 55857035, -325376585, 2001087635, -11762385185, 71795014235, -424666569785, 2578516996835, -15318514090385, 92674023995435, -552229446706985

Offset: 0

Author

Philippe Deléham, Oct 08 2009

Keywords

• easy
• sign

Comments

From Klaus Brockhaus, Oct 14 2009: (Start)

Fourth binomial transform of A014992.

Sixth binomial transform is A001020 preceded by 1.

Lim_{n -> infinity} a(n)/a(n-1) = -6. (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (-1,30).

Crossrefs

Cf. A166035, A166036.

Cf. A014992 (q-integers for q=-10), A001020 (powers of 11).

Programs

Magma

[(5^n+10*(-6)^n)/11: n in [0..30]]; // Vincenzo Librandi, May 02 2011

Mathematica

CoefficientList[Series[(1-4x)/(1+x-30x^2), {x,0,40}], x]  (* Harvey P. Dale, Mar 11 2011 *)
LinearRecurrence[{-1,30},{1,-5},20] (* Harvey P. Dale, Jan 20 2022 *)

PARI

a(n)=(5^n+10*(-6)^n)/11 \\ Charles R Greathouse IV, May 02 2016

Formula

a(n) = 30*a(n-2)-a(n-1), a(0)= 1, a(1)= -5.

G.f.: (1-4x)/(1+x-30*x^2).

a(n) = Sum_{k=0..n} A112555(n,k)*(-6)^k.

E.g.f.: (1/11)*(exp(5*x) + 10*exp(-6*x)). - G. C. Greubel, May 01 2016