# Revision history [back]

I will elaborate on the comment, which is correct; you could use

sage: def N(d,n):
....:  if n==1:
....:         return 1
....:  else:
....:         return sum(N(d,i) for i in range(1,n))


Ordinarily, this should have just returned some sort of evident error that you couldn't do it (such as below). But because of a subtlety in how you defined your function, instead you never actually discovered this in your sum. Your sum instead kept returning itself when n=2, so you got a RuntimeError about infinite recursion.

If you do sum? in the terminal or notebook, you should get documentation that includes this:

   Warning: This function only works with symbolic expressions. To
sum any other objects like list elements or function return
values, please use python summation, see
http://docs.python.org/library/functions.html#sumIn particular,
this does not work:

sage: n = var('n')
sage: mylist = [1,2,3,4,5]
sage: sum(mylist[n], n, 0, 3)
Traceback (most recent call last):
...
TypeError: unable to convert n to an integer

Use python "sum()" instead:

sage: sum(mylist[n] for n in range(4))
10


Also, where does d occur in your function? It seems to be a dummy variable in the truest sense of the word - completely silent, that is.

I will elaborate on the comment, other answer, which is correct; you could use

sage: def N(d,n):
....:  if n==1:
....:         return 1
....:  else:
....:         return sum(N(d,i) for i in range(1,n))


Ordinarily, this should have just returned some sort of evident error that you couldn't do it (such as below). But because of a subtlety in how you defined your function, instead you never actually discovered this in your sum. Your sum instead kept returning itself when n=2, so you got a RuntimeError about infinite recursion.

If you do sum? in the terminal or notebook, you should get documentation that includes this:

   Warning: This function only works with symbolic expressions. To
sum any other objects like list elements or function return
values, please use python summation, see
http://docs.python.org/library/functions.html#sumIn particular,
this does not work:

sage: n = var('n')
sage: mylist = [1,2,3,4,5]
sage: sum(mylist[n], n, 0, 3)
Traceback (most recent call last):
...
TypeError: unable to convert n to an integer

Use python "sum()" instead:

sage: sum(mylist[n] for n in range(4))
10


Also, where does d occur in your function? It seems to be a dummy variable in the truest sense of the word - completely silent, that is.