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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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1898-9934
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Volume 14, Issue 4

Issues

The Catalan Numbers. Part II1

Karol Pąk
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, Volume 14, Issue 4, Pages 153–159, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0019-7.

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