---
tag: YVSHKW70P6
kind: concept
name: Coins in a fountain
sources:
  - wikipedia: en:42922966@r1363061248
    locator: Coins in a fountain
    note: adopted
    mention: wikipedia://en/42922966
    sections: [Summary]
same_as:
  wikidata: Q18348232
  wikipedia: Coins in a fountain
inventory: [7HH7Y00W4P]
---

## Summary

**Coins in a fountain** is a problem in [[combinatorial|0JKW7W7XFR]] mathematics involving a [[generating function|0HH6JX5WZZ]]. In this problem, a *fountain* is an arrangement of non-overlapping coins, modeled as unit circles, into horizontal rows in the plane. Consecutive coins in the bottom row are tangent to each other, and each coin in a higher row is tangent to two coins in the row immediately below it. Above the bottom row, consecutive coins are not required to touch. The problem asks for the number of different fountains of $n$ coins with $k$ coins in the bottom row.