[ProjectEuler] Problem 621: Expressing an integer as the sum of triangular numbers

Statement:

• 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 × 10^9).

Proof of Integer is Sum of Three Triangular Numbers:

• https://proofwiki.org/wiki/Integer_is_Sum_of_Three_Triangular_Numbers