Fountain

An fountain is an arrangement of coins in rows such that exactly coins are in the bottom row and each coin in the st row touches exactly two in the th row. For example, a (21, 10) fountain is illustrated above.

A generalized Rogers-Ramanujan-type continued fraction is closely related to the enumeration of coins in a fountain (Berndt 1985).

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References

Berndt, B. C. Ramanujan's Notebooks, Part III. New York: Springer-Verlag, p. 79, 1985.Berndt, B. C.; Huang, S.-S.; Sohn, J.; and Son, S. H. "Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook." Trans. Amer. Math. Soc. 352, 2157-2177, 2000.Guy, R. "The Strong Law of Small Numbers." Amer. Math. Monthly 95, 697-712, 1988.Odlyzko, A. M. and Wilf H. S. "

Coins in a Fountain." Amer. Math. Monthly 95, 840-843, 1988.

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Fountain

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Weisstein, Eric W. "Fountain." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Fountain.html

Fountain

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