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.

A122007 Expansion of 2*x^2*(1-2*x) / ((3*x-1)*(3*x^2-1)).

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%I A122007 #14 Sep 23 2016 11:03:36
%S A122007 0,2,2,12,24,90,234,756,2160,6642,19602,59292,176904,532170,1593594,
%T A122007 4785156,14346720,43053282,129133602,387440172,1162241784,3486843450,
%U A122007 10460294154,31381236756,94143001680,282430067922,847288078002,2541867422652,7625595890664
%N A122007 Expansion of 2*x^2*(1-2*x) / ((3*x-1)*(3*x^2-1)).
%D A122007 "Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.
%H A122007 Colin Barker, <a href="/A122007/b122007.txt">Table of n, a(n) for n = 1..1000</a>
%H A122007 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-9).
%F A122007 Limit a(n+1)/a(n)= 3 as n-> infinity.
%F A122007 a(n)= 3*a(n-1) +3*a(n-2) -9*a(n-3) = 3^(n-2) + (-1)^n*A108411(n-2), n>=2.
%F A122007 From _Colin Barker_, Sep 23 2016: (Start)
%F A122007 a(n) = 3^(n/2-1)+3^(n-2) for n>1 and even.
%F A122007 a(n) = 3^(n-2)-3^((n-3)/2) for n>1 and odd.
%F A122007 (End)
%t A122007 M = {{0, 1, 2}, {1, 2, 0}, {2, 0, 1}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[3]], {n, 1, 50}]
%o A122007 (PARI) concat(0, Vec(2*x^2*(1-2*x)/((3*x-1)*(3*x^2-1)) + O(x^40))) \\ _Colin Barker_, Sep 23 2016
%K A122007 nonn,easy
%O A122007 1,2
%A A122007 _Roger L. Bagula_ and _Gary W. Adamson_, Sep 11 2006
%E A122007 Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010
%E A122007 A-number in formula corrected - _R. J. Mathar_, Mar 30 2010