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.

A047085 a(n) = T(2*n, n), array T as in A047080.

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%I A047085 #17 Oct 31 2022 07:33:53
%S A047085 1,1,3,9,27,83,259,817,2599,8323,26797,86659,281287,915907,2990383,
%T A047085 9786369,32092959,105435607,346950321,1143342603,3772698725,
%U A047085 12463525229,41218894577,136451431723,452116980643,1499282161375,4975631425581,16524213199923,54913514061867
%N A047085 a(n) = T(2*n, n), array T as in A047080.
%H A047085 G. C. Greubel, <a href="/A047085/b047085.txt">Table of n, a(n) for n = 0..1000</a>
%F A047085 From _G. C. Greubel_, Oct 30 2022: (Start)
%F A047085 a(n) = A171155(n).
%F A047085 G.f.: sqrt((1 - x)/(1 - 3*x - x^2 - x^3)). (End)
%t A047085 CoefficientList[Series[Sqrt[(1-x)/(1-3*x-x^2-x^3)], {x, 0, 50}], x] (* _G. C. Greubel_, Oct 30 2022 *)
%o A047085 (Magma) R<x>:=PowerSeriesRing(Rationals(), 50); Coefficients(R!( Sqrt((1-x)/(1 -3*x-x^2-x^3)) )); // _G. C. Greubel_, Oct 30 2022
%o A047085 (SageMath)
%o A047085 def A047085_list(prec):
%o A047085     P.<x> = PowerSeriesRing(ZZ, prec)
%o A047085     return P( sqrt((1-x)/(1-3*x-x^2-x^3)) ).list()
%o A047085 A047085_list(50) # _G. C. Greubel_, Oct 30 2022
%Y A047085 Cf. A047080, A047081, A047082, A047083, A047084, A047086, A047087, A047088.
%Y A047085 Cf. A171155.
%K A047085 nonn
%O A047085 0,3
%A A047085 _Clark Kimberling_
%E A047085 Data corrected by _Sean A. Irvine_, May 11 2021