A161718 Expansion of (1+3*x^2)/(1+x)^2.

1, -2, 6, -10, 14, -18, 22, -26, 30, -34, 38, -42, 46, -50, 54, -58, 62, -66, 70, -74, 78, -82, 86, -90, 94, -98, 102, -106, 110, -114, 118, -122, 126, -130, 134, -138, 142, -146, 150, -154, 158, -162, 166, -170, 174, -178, 182, -186, 190, -194, 198, -202, 206, -210, 214, -218, 222, -226, 230, -234

Offset: 0

Author

Pr Mosbah Amlouk (Mosbah.Amlouk(AT)fsb.rnu.tn), Jun 17 2009

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-2,-1).

Crossrefs

Cf. A016825, A111284 (unsigned version), A135929, A137276.

Programs

Mathematica

CoefficientList[Series[(1+3*x^2)/(1+x)^2,{x,0,80}],x] (* or *) LinearRecurrence[ {-2,-1},{1,-2,6},80] (* Harvey P. Dale, Mar 19 2016 *)

PARI

x='x+O('x^99); Vec((1+3*x^2)/(1+x)^2) \\ Altug Alkan, Apr 17 2018

Formula

From R. J. Mathar, Aug 27 2009: (Start)

a(n) = -2*a(n-1)-a(n-2), n>3.

G.f.: (1+3*x^2)/(1+x)^2.

a(n) = 4*(-1)^n*n+2*(-1)^(n+1) = (-1)^n*A016825(n-1), n>0. (End)

E.g.f.: 3 - 2*exp(-x)*(1 + 2*x). - Stefano Spezia, Feb 02 2023

Extensions

Spurious commas in sequence deleted by N. J. A. Sloane, Aug 02 2009

Offset corrected, extended by R. J. Mathar, Aug 27 2009

Edited by Joerg Arndt, Sep 04 2011