# Partition a Number n into k Parts: 7 Possible Solutions

I want to partition a number n into k parts
for example 9 into 3 parts
x+y+z=9
and each element must be non zero , first look tells me it's combination with repetition.
however C(n-1,n-k) doesn't give the same number of possibilities when trying all of them.
x+y+z=9 C(8,6)=28
while trying them give only 7 possibilities
(7,1,1) (6,2,1) (5,2,2) (5,3,1) (4,4,1) (4,3,2) (3,3,3)
(1,7,1) is the same as (1,1,7) and (7,1,1) this small condition is changing the outcome , what kind of problem is this called ?

I want to partition a number n into k parts
for example 9 into 3 parts
x+y+z=9
and each element must be non zero , first look tells me it's combination with repetition.

9 into 3 positive parts, is the same as 6 into 3 nonnegative parts, which is http://www.research.att.com/~njas/sequences/A038505 [Broken] (6) = 28. I don't know a term for this better than "partitioning".

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first thing , i didn't quiet understand what this is , plus i already stated that the number actually is 7 not 28.
any help with what I'm dealing with here?

if you really "partitioning" that I believe that (1,1,7), (1,7,1) and (7,1,1) are identical in this context. nCr doesn't work because you have an addition constraint namely, x+y+z=constant. There is also a generalised version of this problem where you partition a number into$$N$$ parts (not just 3) where $$N\geq 1$$. more interesting properties will ensure there too.

already find some stuff , but one question , in what language is this program written in?
INPUT m
DIM a(m),p(m)
FOR i = 0 TO m: p(i) = 1: NEXT i

FOR u = 2 TO m
FOR i = 0 TO m: a(i) = p(i): p(i) = 0: NEXT i
FOR j = 0 TO m STEP u
FOR k = j TO m
p(k) = p(k) + a(k-j)
NEXT k
NEXT j
NEXT u

REM

I think it looks like qbasic