# Function for finding addition decompositions of an integer

**URL:** <https://discourse.julialang.org/t/function-for-finding-addition-decompositions-of-an-integer/60295>\
**Category:** New to Julia\
**Created:** [April 30, 2021, 9:20am UTC](https://discourse.julialang.org/t/function-for-finding-addition-decompositions-of-an-integer/60295 "2021-04-30T09:20:56Z")\
**Posts on this page:** 1\
**Showing post:** 3

<div class="post-metadata">

**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [April 30, 2021, 10:19am UTC](https://discourse.julialang.org/t/function-for-finding-addition-decompositions-of-an-integer/60295/3 "2021-04-30T10:19:55Z")

</div>

Using [Combinatorics.jl](https://github.com/JuliaMath/Combinatorics.jl) (_and collect-free after @DNF’s advice_):

```julia
using Combinatorics

function sum_combinations(N)
    list = Vector{Int64}[]
    for i in 2:N
        for x in combinations(1:N,i)
            if sum(x) == N
                push!(list, x)
            end
        end
    end
    return list
end

julia> sum_combinations(7)
4-element Vector{Vector{Int64}}:
 [1, 6]
 [2, 5]
 [3, 4]
 [1, 2, 4]

```

---

_[View the full topic](https://discourse.julialang.org/t/function-for-finding-addition-decompositions-of-an-integer/60295)._