How this calculation works
Count distributions of identical items to labeled boxes with a per-box cap.
THE FORMULA
Count ways to extend each partial sum with a value from 0 through the box capA worked example
Six items in three boxes capped at three yield ten allocations.
Good to know
Empty boxes are allowed. Each box has the same cap.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count distributions of identical items to labeled boxes with a per-box cap.
The primary result is labeled “Allocations”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Empty boxes are allowed. Each box has the same cap.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Six items in three boxes capped at three yield ten allocations.
Which rule does this calculator apply?
Count ways to extend each partial sum with a value from 0 through the box cap