A180086 Sum of n and floor of each previous term divided by its distance from n.

1, 3, 6, 11, 20, 33, 54, 87, 142, 226, 360, 571, 907, 1438, 2278, 3606, 5708, 9032, 14293, 22614, 35778, 56604, 89550, 141670, 224122, 354560, 560907, 887348, 1403768, 2220731, 3513149, 5557726, 8792197, 13909055, 22003808, 34809515, 55067847, 87116054, 137815571

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Formula

a(n) = n + floor(a(n-1)/1) + floor(a(n-2)/2) + ... + floor(a(1)/(n-1)).

Example

a(1) = 1 by definition.
a(4) = 4 + a(3)/1 + floor(a(2)/2) + floor(a(1)/3) = 4 + 6 + floor(3/2) + floor(1/3) = 11.

Maple

a:= proc(n) option remember; `if`(n=1, 1,
      n+add(floor(a(n-j)/j), j=1..n-1))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, Apr 01 2025

Crossrefs

Sequence in context: A191696 A252479 A320850 * A116365 A297443 A185083

Adjacent sequences: A180083 A180084 A180085 * A180087 A180088 A180089

Keyword

nonn

Author

Dominick Cancilla, Aug 09 2010

Extensions

Offset changed to 1 by Georg Fischer, Apr 01 2025

Status

approved