An -fountain is an arrangement of coins in which each coin above the bottom row rests on two coins on the row below. For , the number of -fountains is .

An -fountain with coins in its base is sometimes called an -fountain. For a given , the widest fountain is just a bottom row of coins—an -fountain—and the tallest, narrowest fountain fills as much of a triangle as possible. Between the extremes, there are typically multiple -fountains.

References

[1] R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge: Cambridge University Press, 1999 p. 228.

[2] S. R. Finch, Mathematical Constants, Cambridge: Cambridge University Press, 2003 pp. 380–381.

[3] "A005169." The On-Line Encyclopedia of Integer Sequences. (Feb 15, 2012) oeis.org/A005169.