The Catalan Numbers. Part II 1

Karol Pąk

Formalized Mathematics (2006)

  • Volume: 14, Issue: 4, page 153-159
  • ISSN: 1426-2630

Abstract

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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

How to cite

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Karol Pąk. " The Catalan Numbers. Part II 1 ." Formalized Mathematics 14.4 (2006): 153-159. <http://eudml.org/doc/266549>.

@article{KarolPąk2006,
abstract = {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},
author = {Karol Pąk},
journal = {Formalized Mathematics},
language = {eng},
number = {4},
pages = {153-159},
title = { The Catalan Numbers. Part II 1 },
url = {http://eudml.org/doc/266549},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Karol Pąk
TI - The Catalan Numbers. Part II 1
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 4
SP - 153
EP - 159
AB - 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
LA - eng
UR - http://eudml.org/doc/266549
ER -

References

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