A349015 G.f. A(x) satisfies: A(x) = 1 + x * A(x) / (1 - x) - x * A(x)^2.

1, 0, 1, 0, 2, -1, 5, -6, 16, -28, 62, -125, 267, -565, 1213, -2618, 5686, -12418, 27248, -60048, 132848, -294930, 656878, -1467257, 3286219, -7378239, 16603459, -37441989, 84599855, -191501531, 434224405, -986161958, 2243009870, -5108859820, 11651743902

Offset

0,5

Links

Table of n, a(n) for n=0..34.

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} a(k) * (1 - a(n-k-1)).

a(n) = 1 - Sum_{k=0..n-1} (-1)^k * A007477(k).

a(n) ~ 3^(1 + n) * (1/((1 - 2/(19 - 3*sqrt(33))^(1/3) - (1/2)*(19 - 3*sqrt(33))^(1/3))^n * ((19 - 3*sqrt(33))^(1/6)*(2 + (19 - 3*sqrt(33))^(1/3))^2 * n^(3/2) * sqrt(((-1951699 + 339747*sqrt(33))*Pi) / (-70717234 + 12310290*sqrt(33) + (19 - 3*sqrt(33))^(2/3) * (-3903398 + 679494*sqrt(33)) + (19 - 3*sqrt(33))^(1/3) * (-35358617 + 6155145*sqrt(33))))))). - Vaclav Kotesovec, Nov 17 2021

Mathematica

nmax = 34; A[_] = 0; Do[A[x_] = 1 + x A[x]/(1 - x) - x A[x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[a[k] (1 - a[n - k - 1]), {k, 0, n - 1}]; Table[a[n], {n, 0, 34}]

Crossrefs

Cf. A000108, A007477, A215973, A349014, A349016.

Sequence in context: A095242 A357179 A125080 * A217105 A143892 A129321

Adjacent sequences: A349012 A349013 A349014 * A349016 A349017 A349018

Keyword

sign

Author

Ilya Gutkovskiy, Nov 05 2021

Status

approved