Integer Partition Generator
One target number per line - list every addition combination that sums to it, group them by addend count, or count them
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Calculation Result
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| No. | Target | Addends | Combination | Number of combinations |
|---|
Introduction to the tool and how to use it
Mathematical integer partitions: enter a target N and list every positive-integer addition that sums to N. Reordering alone counts as the same partition (5 = 4 + 1 and 5 = 1 + 4 count once), and the count is the partition number p(N).
Partitions grow extremely fast: p(20) = 627, p(50) = 204226, p(200) ≈ 3.97 × 10¹², so a target cap of 200, an output cap on combinations, and a table-row cap are enforced; excess is truncated automatically with a notice. Enumeration is lazy and stops once enough are gathered; counts use BigInt in a two-dimensional recurrence, so even at N up to 200 there is never a precision error.
Partitions grow extremely fast: p(20) = 627, p(50) = 204226, p(200) ≈ 3.97 × 10¹², so a target cap of 200, an output cap on combinations, and a table-row cap are enforced; excess is truncated automatically with a notice. Enumeration is lazy and stops once enough are gathered; counts use BigInt in a two-dimensional recurrence, so even at N up to 200 there is never a precision error.
How to use
- Enter one target per line, such as
5,10,20; you may paste many lines at once. - Choose a mode:
· All partitions: list one by one, such as5 = 4 + 1,5 = 3 + 2,5 = 3 + 1 + 1…;
· Group by number of addends: which partitions use 1 addend, 2 addends, 3 addends, with the true count of each group;
· Count only: return just p(N), such asp(100) = 190569292; - The connector can be changed to
,,|, and so on (left empty it defaults to+). - Results support one-click copy and CSV export.
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