A076040 a(n) = (-1)^n * (3^n - 1)/2.

0, -1, 4, -13, 40, -121, 364, -1093, 3280, -9841, 29524, -88573, 265720, -797161, 2391484, -7174453, 21523360, -64570081, 193710244, -581130733, 1743392200, -5230176601, 15690529804, -47071589413, 141214768240, -423644304721, 1270932914164

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-4,-3).

Formula

Equals A038608 o A003462 = A033999 * A003462, i.e., a(n) = (-1)^n*A003462(n) = (-1)^A003462(n)*A003462(n) = A038608(A003462(n)). - M. F. Hasler, Oct 21 2014

From Colin Barker, Oct 22 2014: (Start)

a(n) = -4*a(n-1) - 3*a(n-2).

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

E.g.f.: (-1)*exp(-2*x)*sinh(x). - G. C. Greubel, Jun 18 2021

Mathematica

Table[(-1)^n*(3^n -1)/2, {n, 0, 30}] (* G. C. Greubel, Jun 18 2021 *)

Prog

(PARI) concat(0, Vec(-x/((x+1)*(3*x+1)) + O(x^100))) \\ Colin Barker, Oct 22 2014
(Sage) [(-1)^n*(3^n -1)/2 for n in (0..30)] # G. C. Greubel, Jun 18 2021

Crossrefs

Cf. A003462, A033999.

Sequence in context: A238846 A025567 A003462 * A261547 A091141 A098183

Adjacent sequences: A076037 A076038 A076039 * A076041 A076042 A076043

Keyword

sign,easy

Author

M. F. Hasler, Oct 21 2014

Extensions

Former duplicate of A003462 changed to the signed variant by M. F. Hasler, Oct 21 2014

Status

approved