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, 0, 1, 1, 4, 9, 27, 76, 226, 680, 2078, 6441, 20153, 63684, 202732, 649930, 2095854, 6794684, 22131765, 72393439, 237703654, 783198068, 2588645047, 8580674778, 28517805357, 95009277576, 317242351135, 1061500510809, 3558683892258, 11952025977378, 40209157279701

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Formula

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

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

Example

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 + ...

Mathematica

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

Crossrefs

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

Sequence in context: A034527 A329155 A111962 * A365609 A198095 A256096

Adjacent sequences: A307525 A307526 A307527 * A307529 A307530 A307531

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 12 2019

Status

approved