Bi-Tri tree

As the root is the only node of height 0,so any node of height n will mean the node has n-1 more ancestors other than the root.It means it is in the n th level after the root. So if n is an even number, however the root is BiParent or TriParent, there will be $2^{n/2}*3^{n/2}$ leaves. If n is odd, if the root is BiParent then there will be $2^{(n+1)/2}*3^{(n-1)/2}$ leaves,else the root is TriParent then there will be $2^{(n-1)/2}*3^{(n+1)/2}$ leaves. So number of leaves will be maximized if the root is TriParent.

Here n=11 which is odd. So the maximum leaf number would be $2^{(11-1)/2}*3^{(11+1)/2}$ = $2^{5}*3^{6}$ =23328

a simple recursion . my c++ code may work well as solution .

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#include<iostream>
using namespace std;
int number( int i)
{

    if(i==0) return 1;
    else return (i%2+2)*number(i-1);
}
int main()
{

    cout<<number(11)<<endl;
    return 0;

}