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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (-2,-1).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A111284 A130824 A016825 * A122905 A132417 A103747

Adjacent sequences: A161715 A161716 A161717 * A161719 A161720 A161721

Keyword

sign,easy

Author

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

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

Status

approved