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.

A115052 Expansion of 1/(3*x^2 - 3*x + 1)^2.

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%I A115052 #33 Sep 01 2025 16:40:46
%S A115052 1,6,21,54,108,162,135,-162,-1053,-2916,-5832,-8748,-8019,4374,41553,
%T A115052 118098,236196,354294,334611,-118098,-1476225,-4251528,-8503056,
%U A115052 -12754584,-12223143,3188646,49424013,143489070,286978140,430467210,416118303,-86093442,-1592728677
%N A115052 Expansion of 1/(3*x^2 - 3*x + 1)^2.
%C A115052 q=1 coefficient expansion of hierarchical lattice renormalization polynomial.
%D A115052 Heinz-Otto Peitgen and Peter Richter (editors), The Beauty of Fractals, Springer-Verlag, New York, 1986, p. 146.
%H A115052 Vincenzo Librandi, <a href="/A115052/b115052.txt">Table of n, a(n) for n = 0..200</a>
%H A115052 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,18,-9).
%F A115052 From _Stefano Spezia_, Sep 01 2025: (Start)
%F A115052 a(n) = 3^(n/2)*((1 - n)*cos(n*Pi/6) + sqrt(3)*(3 + n)*sin(n*Pi/6)).
%F A115052 E.g.f.: exp(3*x/2)*(cos(sqrt(3)*x/2) + sqrt(3)*(3 + 2*x)*sin(sqrt(3)*x/2)). (End)
%p A115052 A115052 := proc(n) 1/(3*x^2-3*x+1)^2 ; coeftayl(%,x=0,n) ; end proc: # _R. J. Mathar_, Sep 17 2011
%o A115052 (Magma) I:=[1,6,21,54]; [n le 4 select I[n] else 6*Self(n-1)-15*Self(n-2)+18*Self(n-3)-9*Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Sep 20 2011
%Y A115052 Autoconvolution of A057083.
%K A115052 sign,easy,changed
%O A115052 0,2
%A A115052 _Roger L. Bagula_, Feb 28 2006