I agree with you. Nevertheles, here is a partial answer to Raman question.
If take a simpler recurrence than yours
1) a_0 = 0, a_1 = 1, b_0 = 1 and b_1 = 0
2) for n >= 0, a_{n+1} = 2 * a_n + b_n and b_{n+2} = a_n + 3 * b_n
@cached_function
def a(n):
if n == 0: return 0
elif n == 1: return 1
else: return 2*a(n-1) + b(n-1)
@cached_function
def b(n):
if n == 0: return 1
elif n == 1: return 0
else: return a(n-1) + 3*b(n-1)
Then running sage you obtain
sage: a(10)
29375
sage: b(10)
47500
The advantage of having cached_function is that each result is stored while
you do not have to take care about it! It is also possible to adapt your
maple code but this recursive version is much more compact.
Vincent
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