Dan's recursion formula is:

P[n]  <= 4*2*P[n-1] + 6*2*P[n-2] + 4*2*P[n-3] + 1*2*P[n-4]

Dan's calculations:

P[0]  =           1
P[1]  =          12
P[2]  =         114
P[3]  =       1,068
P[4]  =      10,011

Ummm.  4*2*P[4-1] + 6*2*P[4-2] + 4*2*P[4-3] + 1*2*P[4-4] =
       4*2*1068 + 6*2*114 + 4*2*12 + 1*2*1 = 10010 < P[4].

What have I missed? Is Dan's formula not valid until n=5 or something?

der Mouse

mouse@collatz.mcrcim.mcgill.edu