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# Problem 621

## Expressing an integer as the sum of triangular numbers

Gauss famously proved that every positive integer can be expressed as the sum of three triangular numbers (including 0 as the lowest triangular number). In fact most numbers can be expressed as a sum of three triangular numbers in several ways.

Let $G(n)$ be the number of ways of expressing $n$ as the sum of three triangular numbers, regarding different arrangements of the terms of the sum as distinct.

For example, $G(9)=7$, as 9 can be expressed as: 3+3+3, 0+3+6, 0+6+3, 3+0+6, 3+6+0, 6+0+3, 6+3+0.
You are given $G(1000)=78$ and $G(10^6)=2106$.

Find $G(17526\times10^9)$.