On Oct 29, 2011, at 9:08 AM, Suleyman K wrote:
Hi,
I am trying to get different combinations of a vector of different
size and
find their sum. For example, if I have a vector (i,j) where i and j
can be
anything from 0 to 5, i get these combinations (0,0), (0,1), (1,0),
(1,1),
(2,0), ...... (5,5) and find sum of these as 0, 1, 1, 2, ..... , 10.
I used
outer functions to get this and it worked. What if I have a vector
(i,j,k)
where all i, j , and k can be anything from 0 to 5. I want to do the
same
thing here. Get all the combinations and sum them up. (0,0,0) (0,0,1),
(0,1,0), (1,0,0), .... (5,5,5) How can I get these combinations and
find
their sums? Thank you very much in advance.
You did say "combinations" rather than permutations, so:
> colSums(combn(0:5, 3))
[1] 3 4 5 6 5 6 7 7 8 9 6 7 8 8 9 10 9 10 11 12
If you instead meant "permutations", then consider this:
> rowSums(expand.grid(0:5,0:5, 0:5))
[1] 0 1 2 3 4 5 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5
6 7 8 4 5 6 7 8 9 5 6 7
[34] 8 9 10 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 8
4 5 6 7 8 9 5 6 7 8 9 10
[67] 6 7 8 9 10 11 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6
7 8 9 5 6 7 8 9 10 6 7 8
[100] 9 10 11 7 8 9 10 11 12 3 4 5 6 7 8 4 5 6 7 8 9
5 6 7 8 9 10 6 7 8 9 10 11
[133] 7 8 9 10 11 12 8 9 10 11 12 13 4 5 6 7 8 9 5 6 7
8 9 10 6 7 8 9 10 11 7 8 9
[166] 10 11 12 8 9 10 11 12 13 9 10 11 12 13 14 5 6 7 8 9 10
6 7 8 9 10 11 7 8 9 10 11 12
[199] 8 9 10 11 12 13 9 10 11 12 13 14 10 11 12 13 14 15
> table(rowSums(expand.grid(0:5,0:5, 0:5)))
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 3 6 10 15 21 25 27 27 25 21 15 10 6 3 1
A056150 Number of combinations for each possible sum when throwing 3
(normal) dice.
http://oeis.org/A056150
Uka
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