Problem 310: Nim Square

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Alice and Bob play the game Nim Square.

Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number of stones from a heap.

The number of stones in the three heaps is represented by the ordered triple (a,b,c).

If 0≤a≤b≤c≤29 then the number of losing positions for the next player is 1160.

Find the number of losing positions for the next player if 0≤a≤b≤c≤100 000.