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

Author

Roger L. Bagula, May 17 2005

Keywords

• nonn
• easy

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).

Crossrefs

A006054 shifted left twice.

Programs

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

Mathematica

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

PARI

Vec( 1/(1-2*x-x^2+x^3) + O(x^66) )  /* Joerg Arndt, Sep 30 2012 */

Sage

def A106805_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-2*x-x^2+x^3) ).list()
A106805_list(35) # G. C. Greubel, Sep 11 2021

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

Extensions

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

Name corrected by Joerg Arndt, Sep 30 2012