OFFSET
0,6
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 * A(x) * (A(x) - 1).
a(n) ~ sqrt((3 - 3*r^3 - 4*r^4 - 2*r^5)/(8*Pi)) / (n^(3/2) * r^(n+3)), where r = 0.5701490701528437821032230160646366013461622472504286581627... is the root of the equation 1 - 2*r^3 - 4*r^4 - 4*r^5 + r^6 = 0. - Vaclav Kotesovec, Jul 03 2021
MATHEMATICA
a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[a[k] a[n - k - 3], {k, 1, n - 3}]; Table[a[n], {n, 0, 42}]
nmax = 42; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 A[x] (A[x] - 1) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 02 2021
STATUS
approved