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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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Volume 14, Issue 4 (Jan 2006)

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The Catalan Numbers. Part II1

Karol Pąk
  • Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-006-0019-7

The Catalan Numbers. Part II1

In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula

and satisfies the recurrence relation

Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0)

Using the above recurrence relation we can see that

where and hence

MML identifier: CATALAN2, version: 7.8.03 4.75.958

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About the article


Published Online: 2008-06-13

Published in Print: 2006-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0019-7. Export Citation

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[1]
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