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
@article{bwmeta1.element.doi-10_2478_v10037-006-0019-7,
author = {Karol P\k ak},
title = {
The Catalan Numbers. Part II
1
},
journal = {Formalized Mathematics},
volume = {14},
year = {2006},
pages = {153-159},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0019-7}
}
Karol Pąk.
The Catalan Numbers. Part II
1
. Formalized Mathematics, Tome 14 (2006) pp. 153-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-006-0019-7/
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