Generate Partition Number Sequence
Create Partition function numbers. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate Partition Number Sequence
- 1. Set how many terms. Enter How many terms to decide the length of the partition number list, the counts of ways each integer can be written as a sum of positive integers, ignoring order.
- 2. Set a separator. Choose Separator, a comma or newline, to shape the output for a plain list or spreadsheet column.
- 3. Copy the results. The tool computes each partition number using Euler's pentagonal number recurrence, a far faster method than enumerating every partition directly. Copy the values for your combinatorics reference.
When to use Generate Partition Number Sequence
Generate Partition Number Sequence lists p(n), the number of distinct ways to write n as a sum of positive integers regardless of order. Reach for it whenever a combinatorics problem needs partition counts without enumerating every possible sum by hand, which becomes impractical quickly.
- Verifying a manual partition count. A student who hand-counted the ways to partition the number 5 checks their tally of 7 against the corresponding term in the generated sequence to confirm they found every partition.
- Testing a pentagonal recurrence implementation. A developer who implemented Euler's pentagonal number recurrence to compute partition numbers efficiently validates the output against known values here to catch a sign error in the recurrence terms.
- Studying generating functions. Someone working through how the partition function relates to an infinite product generating function wants a reference list of p(n) values to check numerical examples against.
- Preparing a number theory course handout. An instructor covering integer partitions wants a printed table of partition numbers to distribute alongside worked examples of the recurrence derivation.
Examples
The partition numbers p(0) through p(10)
Output
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42
About the Generate Partition Number Sequence tool
Generate Partition Number Sequence does its work locally, right in the browser. Create Partition function numbers. There is no upload step, no queue and no account, and your data never travels over the network.
It belongs to the Math Tools collection on EditSafely, a set of 234 small, focused Math utilities that share the same instant, private workspace.
You can shape the output with 2 settings, including How many terms and Separator, and the result refreshes the moment you change one. A worked example further down the page shows exactly what the tool produces for a real input.
Running locally also makes the tool fast and dependable: results appear as you type or drop a file, there is no server outage that can take it down mid-task, and confidential data can be processed without a second thought.
Frequently asked questions
Is Generate Partition Number Sequence free to use?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
Everything happens locally. Your browser downloads the tool's code once, then does all the processing itself; nothing you enter is transmitted, stored or logged. You can even go offline after the page loads and it will still work.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
No. The tool works in any modern browser on desktop, tablet or phone. There is no account to create, no extension to add and no software to install.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.