OFFSET
0,3
COMMENTS
Conjecture: limit of a(n+1)/a(n) = 2.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..2800
Vaclav Kotesovec, Graph a(n+1)/a(n)
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 + 14*x^5 + 26*x^6 + 50*x^7 + ...
such that A(x) = A(x^2 + 2*x^3)/(1-x), where
A(x^2+2*x^3) = 1 + x^2 + 2*x^3 + 2*x^4 + 8*x^5 + 12*x^6 + 24*x^7 + 54*x^8 + 80*x^9 + 158*x^10 + 332*x^11 + 682*x^12 + 1432*x^13 + 2730*x^14 + 5308*x^15 + 10544*x^16 + 20656*x^17 + 41496*x^18 + ...
MATHEMATICA
m = 38; A[_] = 1; Do[A[x_] = A[x^2 + 2 x^3]/(1-x) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, #binary(n)+1, A=subst(A, x, x^2+2*x^3)/(1-x +x*O(x^n))); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2015
STATUS
approved