OFFSET
0,5
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Nov 05 2021
STATUS
approved