A199804 G.f.: 1/(1+x+x^3).

1, -1, 1, -2, 3, -4, 6, -9, 13, -19, 28, -41, 60, -88, 129, -189, 277, -406, 595, -872, 1278, -1873, 2745, -4023, 5896, -8641, 12664, -18560, 27201, -39865, 58425, -85626, 125491, -183916, 269542, -395033, 578949, -848491, 1243524, -1822473, 2670964, -3914488, 5736961, -8407925, 12322413, -18059374, 26467299, -38789712, 56849086, -83316385

Offset

0,4

Comments

There are several similar sequences already in the OEIS, but this one warrants its own entry because it is one of Hirschhorn's family.

Links

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

Michael D. Hirschhorn, Non-trivial intertwined second-order recurrence relations, Fibonacci Quart. 43 (2005), no. 4, 316-325. See K_n.

Index entries for linear recurrences with constant coefficients, signature (-1, 0, -1).

Formula

a(n) = (-1)^n*A000930(n). - R. J. Mathar, Jul 10 2012

G.f.: 1 - x/(G(0) + x) where G(k) = 1 - x^2/(1 - x^2/(x^2 - 1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 16 2012

G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1 - x*(4*k+1 + x^2)/( x*(4*k+3 + x^2) - 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 08 2013

a(0)=1, a(1)=-1, a(2)=1, a(n)=a(n-1)-a(n-3). - Harvey P. Dale, Feb 18 2016

Mathematica

CoefficientList[Series[1/(1+x+x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[ {-1, 0, -1}, {1, -1, 1}, 50] (* Harvey P. Dale, Feb 18 2016 *)

Prog

(PARI) x='x+O('x^50); Vec(1/(1+x+x^3)) \\ G. C. Greubel, Apr 29 2017

Crossrefs

Sequence in context: A000930 A078012 A135851 * A101913 A352042 A121653

Adjacent sequences: A199801 A199802 A199803 * A199805 A199806 A199807

Keyword

sign

Author

N. J. A. Sloane, Nov 10 2011

Status

approved