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 A106805 Expansion of g.f.: 1/(1 - 2*x - x^2 + x^3). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 M= {{0, 0, 1}, {1, 2, 0}, {1, 1, 0}}; v[0]= {0, 1, 1}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[2]], {n, 0, 35}] 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 (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 CROSSREFS A006054 shifted left twice. Sequence in context: A017920 A228765 A006054 * A094981 A304969 A239812 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

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Last modified July 3 04:57 EDT 2022. Contains 355030 sequences. (Running on oeis4.)