An efficient algorithm for generating symmetric ice piles

We define the Symmetric Ice Pile Model  SIPMk(n)SIPMk(n), a generalization of the Ice Pile Model  IPMk(n)IPMk(n), and we show an efficient algorithm for generating the symmetric ice piles with n grains. More precisely, we show how to exploit an existing algorithm for generating IPMk(n)IPMk(n) in order to generate SIPMk(n)SIPMk(n) in amortized time O(1)O(1) and in space O(kn).