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.

A073782 a(n) = Sum_{k=0..n} S(k)*S(n-k), convolution of S=A001644 with itself.

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%I A073782 #11 Sep 08 2022 08:45:06
%S A073782 9,6,19,48,89,190,391,784,1577,3142,6219,12256,24041,46974,91471,
%T A073782 177568,343753,663814,1278979,2459152,4719417,9041470,17294039,
%U A073782 33030320,62999145,120006214,228327099,433939904,823854793,1562602238
%N A073782 a(n) = Sum_{k=0..n} S(k)*S(n-k), convolution of S=A001644 with itself.
%H A073782 G. C. Greubel, <a href="/A073782/b073782.txt">Table of n, a(n) for n = 0..1000</a>
%H A073782 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,0,-3,-2,-1).
%F A073782 G.f.: (3-2*x-x^2)^2/(1-x-x^2-x^3)^2.
%t A073782 CoefficientList[Series[(3-2x-x^2)^2/(1-x-x^2-x^3)^2, {x, 0, 30}], x]
%o A073782 (PARI) my(x='x+O('x^30)); Vec((3-2*x-x^2)^2/(1-x-x^2-x^3)^2) \\ _G. C. Greubel_, Apr 12 2019
%o A073782 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (3-2*x-x^2)^2/(1-x-x^2-x^3)^2 )); // _G. C. Greubel_, Apr 12 2019
%o A073782 (Sage) ((3-2*x-x^2)^2/(1-x-x^2-x^3)^2).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 12 2019
%Y A073782 Cf. A001644.
%K A073782 easy,nonn
%O A073782 0,1
%A A073782 Mario Catalani (mario.catalani(AT)unito.it), Aug 11 2002