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A078027 Expansion of (1-x)/(1-x^2-x^3). 12
1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

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

P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, J. Integer Seqs., Vol. 6, 2003.

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

FORMULA

a(n) is asymptotic to r^(n-2) / (2*r+3) where r = 1.3247179572447..., the real root of x^3 = x + 1. For n >= 4, a(n) = a(n-2) + a(n-3). - Philippe Deléham, Jan 13 2004

a(n) = A182097(n) - A182097(n-1). - R. J. Mathar, Jan 27 2018

MAPLE

seq(coeff(series((1-x)/(1-x^2-x^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 04 2019

MATHEMATICA

CoefficientList[Series[(1-x)/(1-x^2-x^3), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2019 *)

PROG

(PARI) Vec((1-x)/(1-x^2-x^3)+O(x^60)) \\ Charles R Greathouse IV, Sep 23 2012

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x)/(1-x^2-x^3) )); // G. C. Greubel, Aug 04 2019

(Sage) ((1-x)/(1-x^2-x^3)).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Aug 04 2019

(GAP) a:=[1, -1, 1];; for n in [4..60] do a[n]:=a[n-2]+a[n-3]; od; a; # G. C. Greubel, Aug 04 2019

CROSSREFS

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.

Sequence in context: A124745 A133034 A000931 * A134816 A228361 A182097

Adjacent sequences:  A078024 A078025 A078026 * A078028 A078029 A078030

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)