OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: x/((1 - x - x^2) * (x; x)_inf), where (x; x)_inf is the q-Pochhammer symbol.
a(n+1) - a(n) - a(n-1) = A000041(n).
a(n) ~ phi^n / (sqrt(5) * QPochhammer(1/phi)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Sep 27 2016
MATHEMATICA
Table[Sum[Fibonacci[k] PartitionsP[n - k], {k, 1, n}], {n, 0, 30}]
PROG
(PARI) a(n)=sum(k=1, n, fibonacci(k)*numbpart(n - k)); \\ Indranil Ghosh, Jun 29 2017
(Python)
from sympy import fibonacci, npartitions
def a(n): return sum([fibonacci(k)*npartitions(n - k) for k in range(1, n + 1)])
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 29 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Sep 26 2016
STATUS
approved