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.

A026843 a(n) = T(2n,n+3), T given by A026725.

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%I A026843 #18 Sep 08 2022 08:44:49
%S A026843 1,8,46,233,1108,5083,22805,100827,441311,1917751,8289965,35694218,
%T A026843 153225617,656213596,2805143526,11973556060,51047361676,217420991444,
%U A026843 925300665762,3935293406942,16727533586006,71069911887898,301835332909216
%N A026843 a(n) = T(2n,n+3), T given by A026725.
%C A026843 Column k=7 of triangle A236830. - _Philippe Deléham_, Feb 02 2014
%H A026843 G. C. Greubel, <a href="/A026843/b026843.txt">Table of n, a(n) for n = 3..1000</a>
%F A026843 G.f.: (x^3*C(x)^7)/(1-x*C(x)^3) where C(x) is the g.f. of A000108. - _Philippe Deléham_, Feb 02 2014
%F A026843 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 A026843 Drop[CoefficientList[Series[(1-Sqrt[1-4*x])^7/(16*x^2*(8*x^2 -(1-Sqrt[1-4*x])^3)), {x, 0, 40}], x], 3] (* _G. C. Greubel_, Jul 19 2019 *)
%o A026843 (PARI) my(x='x+O('x^40)); Vec( (1-sqrt(1-4*x))^7/(16*x^2*(8*x^2 -(1-sqrt(1-4*x))^3)) ) \\ _G. C. Greubel_, Jul 19 2019
%o A026843 (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1-Sqrt(1-4*x))^7/(16*x^2*(8*x^2 -(1-Sqrt(1-4*x))^3)) )); // _G. C. Greubel_, Jul 19 2019
%o A026843 (Sage) a=((1-sqrt(1-4*x))^7/(16*x^2*(8*x^2 -(1-sqrt(1-4*x))^3)) ).series(x, 45).coefficients(x, sparse=False); a[3:40] # _G. C. Greubel_, Jul 19 2019
%Y A026843 Cf. A000108, A026725, A236830.
%K A026843 nonn
%O A026843 3,2
%A A026843 _Clark Kimberling_