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A077962 Expansion of 1/(1+x^2+x^3). 6

%I #27 Sep 08 2022 08:45:08

%S 1,0,-1,-1,1,2,0,-3,-2,3,5,-1,-8,-4,9,12,-5,-21,-7,26,28,-19,-54,-9,

%T 73,63,-64,-136,1,200,135,-201,-335,66,536,269,-602,-805,333,1407,472,

%U -1740,-1879,1268,3619,611,-4887,-4230,4276,9117,-46,-13393,-9071,13439,22464,-4368,-35903,-18096,40271,53999

%N Expansion of 1/(1+x^2+x^3).

%H G. C. Greubel, <a href="/A077962/b077962.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Janjic/janjic42.html">Determinants and Recurrence Sequences</a>, Journal of Integer Sequences, 2012, Article 12.3.5. [_N. J. A. Sloane_, Sep 16 2012]

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,-1).

%F a(n) = (-1)^n*A077961(n).

%t CoefficientList[ Series[1/(1 + x^2 + x^3), {x, 0, 70}], x] (* _Robert G. Wilson v_, Mar 22 2011 *)

%t LinearRecurrence[{0,-1,-1},{1,0,-1},70] (* _Harvey P. Dale_, Dec 04 2015 *)

%o (PARI) Vec(1/(1+x^2+x^3)+O(x^70)) \\ _Charles R Greathouse IV_, Sep 26 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(1+x^2+x^3) )); // _G. C. Greubel_, Jun 23 2019

%o (Sage) (1/(1+x^2+x^3)).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 23 2019

%o (GAP) a:=[1,0,-1];; for n in [4..70] do a[n]:=-a[n-2]-a[n-3]; od; a; # _G. C. Greubel_, Jun 23 2019

%K sign,easy

%O 0,6

%A _N. J. A. Sloane_, Nov 17 2002

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Last modified April 25 11:39 EDT 2024. Contains 371969 sequences. (Running on oeis4.)