cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A077940 Expansion of 1/(1-2*x+2*x^3).

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%I A077940 #11 Sep 08 2022 08:45:07
%S A077940 1,2,4,6,8,8,4,-8,-32,-72,-128,-192,-240,-224,-64,352,1152,2432,4160,
%T A077940 6016,7168,6016,0,-14336,-40704,-81408,-134144,-186880,-210944,
%U A077940 -153600,66560,555008,1417216,2701312,4292608,5750784,6098944,3612672,-4276224,-20750336,-48726016,-88899584
%N A077940 Expansion of 1/(1-2*x+2*x^3).
%H A077940 G. C. Greubel, <a href="/A077940/b077940.txt">Table of n, a(n) for n = 0..1000</a>
%H A077940 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2).
%F A077940 a(n) = (-1)^n * A077988(n). - _R. J. Mathar_, Feb 04 2014
%t A077940 LinearRecurrence[{2,0,-2}, {1,2,4}, 50] (* or *) CoefficientList[Series[ 1/(1-2*x+2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Jun 26 2019 *)
%o A077940 (PARI) my(x='x+O('x^50)); Vec(1/(1-2*x+2*x^3)) \\ _G. C. Greubel_, Jun 26 2019
%o A077940 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-2*x+2*x^3) )); // _G. C. Greubel_, Jun 26 2019
%o A077940 (Sage) (1/(1-2*x+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 26 2019
%o A077940 (GAP) a:=[1,2,4];; for n in [4..50] do a[n]:=2*(a[n-1]-a[n-3]); od; a; # _G. C. Greubel_, Jun 26 2019
%Y A077940 Cf. A077988.
%K A077940 sign,easy
%O A077940 0,2
%A A077940 _N. J. A. Sloane_, Nov 17 2002