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

%I #24 Nov 08 2022 04:32:39

%S 1,2,5,11,25,56,126,283,636,1429,3211,7215,16212,36428,81853,183922,

%T 413269,928607,2086561,4688460,10534874,23671647,53189708,119516189,

%U 268550439,603427359,1355888968,3046654856,6845771321,15382308530,34563733525,77664004259

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

%C Essentially the same as A006054. - _Joerg Arndt_, Nov 08 2022

%H G. C. Greubel, <a href="/A106805/b106805.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1).

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

%t LinearRecurrence[{2,1,-1}, {1,2,5}, 35] (* _Vladimir Joseph Stephan Orlovsky_, Feb 13 2012 *)

%o (PARI) Vec( 1/(1-2*x-x^2+x^3) + O(x^66) ) /* _Joerg Arndt_, Sep 30 2012 */

%o (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

%o (Sage)

%o def A106805_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P( 1/(1-2*x-x^2+x^3) ).list()

%o A106805_list(35) # _G. C. Greubel_, Sep 11 2021

%Y A006054 shifted left twice.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, May 17 2005

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

%E Name corrected by _Joerg Arndt_, Sep 30 2012

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)