A106805 Expansion of g.f.: 1/(1 - 2*x - x^2 + x^3).

1, 2, 5, 11, 25, 56, 126, 283, 636, 1429, 3211, 7215, 16212, 36428, 81853, 183922, 413269, 928607, 2086561, 4688460, 10534874, 23671647, 53189708, 119516189, 268550439, 603427359, 1355888968, 3046654856, 6845771321, 15382308530, 34563733525, 77664004259

Offset

0,2

Comments

Essentially the same as A006054. - Joerg Arndt, Nov 08 2022

Links

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

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

Formula

G.f. for sequence with 1 prepended: 1/( 1 - Sum_{k>=0} x*(x+x^2-x^3)^k ). - Joerg Arndt, Sep 30 2012

Mathematica

LinearRecurrence[{2, 1, -1}, {1, 2, 5}, 35] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)

Prog

(PARI) Vec( 1/(1-2*x-x^2+x^3) + O(x^66) )  /* Joerg Arndt, Sep 30 2012 */
(Magma) I:=[1, 2, 5]; [n le 3 select I[n] else 2*Self(n-1) +Self(n-2) -Self(n-3): n in [1..36]]; // G. C. Greubel, Sep 11 2021
(SageMath)
def A106805_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-x^2+x^3) ).list()
A106805_list(35) # G. C. Greubel, Sep 11 2021

Crossrefs

A006054 shifted left twice.

Sequence in context: A017920 A228765 A006054 * A356846 A094981 A304969

Adjacent sequences: A106802 A106803 A106804 * A106806 A106807 A106808

Keyword

nonn,easy

Author

Roger L. Bagula, May 17 2005

Extensions

Edited by the Associate Editors of the OEIS, Apr 09 2009

Name corrected by Joerg Arndt, Sep 30 2012

Status

approved