Partition Number Calculator

How many sums equal n?

n (0–60)

p(10)

H-R ≈ 48

All Partitions

109+18+28+1+17+37+2+17+1+1+16+46+3+16+2+26+2+1+16+1+1+1+15+55+4+15+3+25+3+1+15+2+2+15+2+1+1+15+1+1+1+1+14+4+24+4+1+14+3+34+3+2+14+3+1+1+14+2+2+24+2+2+1+14+2+1+1+1+14+1+1+1+1+1+13+3+3+13+3+2+23+3+2+1+13+3+1+1+1+13+2+2+2+13+2+2+1+1+13+2+1+1+1+1+13+1+1+1+1+1+1+12+2+2+2+22+2+2+2+1+12+2+2+1+1+1+12+2+1+1+1+1+1+1

Sequence

p(0)1

p(1)1

p(2)2

p(3)3

p(4)5

p(5)7

p(6)11

p(7)15

p(8)22

p(9)30

p(10)42

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About Partition Number Calculator

A partition number calculator computing p(n) via dynamic programming. p(1)=1, p(2)=2, p(3)=3, p(4)=5, p(5)=7. Hardy-Ramanujan asymptotic: p(n) ~ exp(π√(2n/3))/(4n√3). Euler's generating function: Π(1-x^k)^{-1}. Client-side.

Partition Number Calculator Features

p(n) value
All partitions
Hardy-Ramanujan
Sequence
Distinct parts

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