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.

A026857 a(n) = T(2n+1,n+4), T given by A026736.

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%I A026857 #11 Sep 08 2022 08:44:49
%S A026857 1,9,55,287,1381,6343,28313,124083,537242,2307118,9852240,41910428,
%T A026857 177807902,752981956,3184773246,13459063660,56849094136,240047748038,
%U A026857 1013452871316,4278470305930,18062827159136,76263743441314,322033566728056
%N A026857 a(n) = T(2n+1,n+4), T given by A026736.
%H A026857 G. C. Greubel, <a href="/A026857/b026857.txt">Table of n, a(n) for n = 3..1000</a>
%F A026857 G.f.: x^3*C(x)^8/(1 - x/sqrt(1-4*x)). - _G. C. Greubel_, Jul 19 2019
%F A026857 a(n) ~ phi^(3*n-4) / sqrt(5), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jul 19 2019
%t A026857 Drop[CoefficientList[Series[(1-Sqrt[1-4x])^8/(2^8*x^5*(1-x/Sqrt[1-4x])), {x, 0, 40}], x], 3] (* _G. C. Greubel_, Jul 19 2019 *)
%o A026857 (PARI) my(x='x+O('x^40)); Vec((1-sqrt(1-4*x))^8/(2^8*x^5*(1-x/sqrt(1-4*x)))) \\ _G. C. Greubel_, Jul 19 2019
%o A026857 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^8/(2^8*x^5*(1-x/Sqrt(1-4*x))) )); // _G. C. Greubel_, Jul 19 2019
%o A026857 (Sage) a=((1-sqrt(1-4*x))^8/(2^8*x^5*(1-x/sqrt(1-4*x)))).series(x, 45).coefficients(x, sparse=False); a[3:40] # _G. C. Greubel_, Jul 19 2019
%Y A026857 Cf. A000108, A026736.
%K A026857 nonn
%O A026857 3,2
%A A026857 _Clark Kimberling_