The number of sequences with Nonnegative partial sums which can be formed from 1s and s (Bailey 1996,
Brualdi 1992) is given by the Catalan Numbers. Bailey (1996) gives the number of Nonnegative
partial sums of 1s and s , , ..., , so that

(1) |

(2) |

(3) |

(4) |

(5) |

**References**

Bailey, D. F. ``Counting Arrangements of 1's and 's.'' *Math. Mag.* **69**, 128-131, 1996.

Brualdi, R. A. *Introductory Combinatorics, 2nd ed.* New York: Elsevier, 1992.

© 1996-9

1999-05-25