OFFSET
1,2
LINKS
Vaclav Kotesovec, Plot of a(n)/n for n = 1..100000
FORMULA
G.f.: (1/(1 - x)) * Sum_{k>=2} x^Fibonacci(k)/(1 - x^Fibonacci(k)). - Ilya Gutkovskiy, Jul 16 2019
Conjecture: a(n) ~ c * n, where c = A079586 - 1. - Vaclav Kotesovec, Aug 30 2021
EXAMPLE
a(15)=[ 15/1 ]+[ 15/2 ]+[ 15/3 ]+[ 15/5 ]+[ 15/8 ]+[ 15/13 ]+[ 15/21 ]+...=32.
MAPLE
with(combinat): for n from 1 to 200 do printf(`%d, `, sum(floor(n/fibonacci(k)), k=2..15)) od:
MATHEMATICA
Table[Sum[Floor[n/Fibonacci[k] ], {k, 2, 200}], {n, 70}] (* Harvey P. Dale, Jul 21 2021 *)
Table[Sum[Floor[n/Fibonacci[k]], {k, 2, Log[Sqrt[5]*n]/Log[GoldenRatio] + 1}], {n, 1, 100}] (* Vaclav Kotesovec, Aug 30 2021 *)
PROG
(Magma) [&+[Floor(n/Fibonacci(k+2)):k in [0..n]]:n in [1..64]]; // Marius A. Burtea, Jul 16 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antreas P. Hatzipolakis (xpolakis(AT)hol.gr)
EXTENSIONS
More terms from Simon Plouffe, who points out that the first differences give A005086
More terms from James A. Sellers, Feb 19 2001
STATUS
approved