This question doesn't support checking answers.

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 $G(17 526 \times 10^9)$.