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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). 1

%I #7 Apr 13 2019 08:09:41

%S 1,0,1,1,4,9,27,76,226,680,2078,6441,20153,63684,202732,649930,

%T 2095854,6794684,22131765,72393439,237703654,783198068,2588645047,

%U 8580674778,28517805357,95009277576,317242351135,1061500510809,3558683892258,11952025977378,40209157279701

%N 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 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=2} A000073(k)*x^k*A(x)^k.

%F G.f.: A(x) = (1/x)*Series_Reversion(x*(1 - x - x^2 - x^3)/(1 - x - x^3)).

%e 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 terms = 31; CoefficientList[1/x InverseSeries[Series[x (1 - x - x^2 - x^3)/(1 - x - x^3), {x, 0, terms}], x], x]

%t 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 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 Cf. A000073, A049124, A049140, A307411, A307412, A307413, A307529.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Apr 12 2019

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)