I am having a problem with the online version of PURRS. I tried it on a recurrence relation derived from an algorithm I'm working on, and the resulting formula is off by one for even n. I believe it may be something to do with our assumptions for the base cases and starting index. Is that something that would affect the results?
INPUT: x(n) = x(n-2) + 2*n - 5 for n > 2 x(n) = 0 for n <= 2
OUTPUT: Exact solution for x(n) = -5+x(-2+n)+2*n x(n) = 1/2*n^2+3/2*mod(n,2)+x(mod(n,2))-1/2*mod(n,2)^2-3/2*n
RESULTS: (n, x(n) Recurrence, x(n) PURRS) (2, 0, -1) (3, 1, 1) (4, 3, 2) (5, 6, 6) (6, 10, 9) (7, 15, 15) (8, 21, 20) (9, 28, 28) (10, 36, 35)
Note that the PURRS result is one less when n is even. However, the formula works when the base cases are x(0) = 1 and x(1) = 0. In the results shown above, my assumption is that both are equal to zero.
Thanks and Happy Holidays, Shailesh