Compositions Calculator

2^(n-1) ordered sums

All Tools

n (1–10)

Compositions of 5

= 2^4

By # of Parts

1 parts: 1 = C(4,0)2 parts: 4 = C(4,1)3 parts: 6 = C(4,2)4 parts: 4 = C(4,3)5 parts: 1 = C(4,4)

All Compositions

1 + 1 + 1 + 1 + 1

1 + 1 + 1 + 2

1 + 1 + 2 + 1

1 + 1 + 3

1 + 2 + 1 + 1

1 + 2 + 2

1 + 3 + 1

1 + 4

2 + 1 + 1 + 1

2 + 1 + 2

2 + 2 + 1

2 + 3

3 + 1 + 1

3 + 2

4 + 1

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About Compositions Calculator

A compositions calculator listing all ordered sums k₁+k₂+...+kₘ = n with kᵢ≥1. Unlike partitions, order matters: 2+1 ≠ 1+2. Total: 2^(n-1). Shows all compositions, counts by number of parts, and restricted compositions. Client-side.

Compositions Calculator Features

All compositions
Count 2^(n-1)
Parts count
Restricted
Weak compositions

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