## Golomb's self-describing sequence

### Problem 341

Published on Sunday, 5th June 2011, 10:00 am; Solved by 508

The Golomb's self-describing sequence {G(n)} is the only nondecreasing sequence of natural numbers such that n appears exactly G(n) times in the sequence. The values of G(n) for the first few n are

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | …
G(n) | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 6 | 6 | …

You are given that G(103) = 86, G(106) = 6137.
You are also given that ΣG(n3) = 153506976 for 1 n 103.

Find ΣG(n3) for 1 n 106.