A038663 [ n/F_2 ] + [ n/F_3 ] + [ n/F_4 ] +..., F_n=Fibonacci numbers.

1, 3, 5, 7, 9, 12, 13, 16, 18, 21, 22, 25, 27, 29, 32, 35, 36, 39, 40, 43, 46, 48, 49, 53, 55, 58, 60, 62, 63, 67, 68, 71, 73, 76, 78, 81, 82, 84, 87, 91, 92, 96, 97, 99, 102, 104, 105, 109, 110, 113, 115, 118, 119, 122, 125, 128, 130, 132, 133, 137, 138, 140, 143, 146

Offset

1,2

Links

Table of n, a(n) for n=1..64.

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

Cf. A005086.

Sequence in context: A079091 A353149 A191749 * A291154 A246405 A190328

Adjacent sequences: A038660 A038661 A038662 * A038664 A038665 A038666

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