George Andrews kindly reminds me that The result: # partitions of n into ordered 4tuples of triangular numbers

= sum of divisors of 2n+1.

is due to Legendre. OK, here's one that isn't Legendre's: The Minsky "circle" recurrence x[0] = 0, y[0]=8, x[n+1] = x[n] - floor(2450365*y[n]/1120052), y[n+1] = y[n] + floor(12497*x[n+1]/8798) has period 51284705405843 (= 7 * 13 * 563568191273). The first multiplier was found by tutor Corey's automatic mapper. I chose the second multiplier in an attempt to *avoid* huge periods. --rwg