Integer Partition Count Calculator

Build counts from zero upward, introducing each allowed positive part once so permutations of one sum are not recounted. The empty sum makes p(0) equal one, while no positive parts sum to a negative integer. Inputs must be whole numbers inside the displayed safe bound. The calculator does not round decimals into the domain or silently substitute a different convention, so verify each entered integer before interpreting the exact result.

The output counts additive partitions of an integer, not ordered compositions and not partitions of a labelled set. For small n, list sums in descending-part order to avoid counting rearrangements twice. Use the displayed factors, recurrence step, or modular residue as an independent check. Exact integer output means the implemented arithmetic has no decimal approximation within its bound; it does not prove an unrelated theorem or an unstated combinatorial model.

The input is capped at 100 so the dynamic program remains fast and the returned count remains an exact safe integer. The cap avoids presenting large rounded sequence terms as exact JavaScript integers. The bound keeps browser work predictable and every returned integer within JavaScript's exact safe range. Larger inputs need arbitrary-precision software, explicit resource controls, and independent verification rather than treating an overflowed floating-point value as exact.