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.

A307528 G.f. A(x) satisfies: A(x) = 1 + x^2*A(x)^2/(1 - x*A(x) - x^2*A(x)^2 - x^3*A(x)^3).

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%I A307528 #7 Apr 13 2019 08:09:41
%S A307528 1,0,1,1,4,9,27,76,226,680,2078,6441,20153,63684,202732,649930,
%T A307528 2095854,6794684,22131765,72393439,237703654,783198068,2588645047,
%U A307528 8580674778,28517805357,95009277576,317242351135,1061500510809,3558683892258,11952025977378,40209157279701
%N A307528 G.f. A(x) satisfies: A(x) = 1 + x^2*A(x)^2/(1 - x*A(x) - x^2*A(x)^2 - x^3*A(x)^3).
%F A307528 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=2} A000073(k)*x^k*A(x)^k.
%F A307528 G.f.: A(x) = (1/x)*Series_Reversion(x*(1 - x - x^2 - x^3)/(1 - x - x^3)).
%e A307528 G.f.: A(x) = 1 + x^2 + x^3 + 4*x^4 + 9*x^5 + 27*x^6 + 76*x^7 + 226*x^8 + 680*x^9 + 2078*x^10 + ...
%t A307528 terms = 31; CoefficientList[1/x InverseSeries[Series[x (1 - x - x^2 - x^3)/(1 - x - x^3), {x, 0, terms}], x], x]
%t A307528 terms = 30; A[_] = 0; Do[A[x_] = 1 + x^2 A[x]^2/(1 - x A[x] - x^2 A[x]^2 - x^3 A[x]^3) + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]
%t A307528 terms = 31; t[n_] := t[n] = SeriesCoefficient[x^2/(1 - x - x^2 - x^3), {x, 0, n}]; A[_] = 0; Do[A[x_] = 1 + Sum[t[k] x^k A[x]^k, {k, 2, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y A307528 Cf. A000073, A049124, A049140, A307411, A307412, A307413, A307529.
%K A307528 nonn
%O A307528 0,5
%A A307528 _Ilya Gutkovskiy_, Apr 12 2019