The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A127153 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A127153

Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n and having k UDUD's starting at level 0; here U=(1,1), D=(1,-1) (0<=k<=n-1).
(history; published version)

#14 by Bruno Berselli at Tue Oct 27 05:25:02 EDT 2015

STATUS

editing

approved

#13 by Bruno Berselli at Tue Oct 27 05:24:59 EDT 2015

FORMULA

G.f.: (1+z-t*z)/(1+z-t*z+z^2-t*z^2-z*C(1+z-t*z)9, ), where C = (1-sqrt(1-4*z))/(2*z) is the Catalan g.f. (see A000108).

STATUS

approved

editing

#12 by Bruno Berselli at Tue Oct 27 05:24:29 EDT 2015

STATUS

editing

approved

#11 by Bruno Berselli at Tue Oct 27 05:24:24 EDT 2015

FORMULA

G.f.: (1+z-t*z)/[(1+z-t*z+z^2-t*z^2-z*C(1+z-t*z)], 9, where C = [(1-sqrt(1-4*z)])/(2*z) is the Catalan g.f. (see A000108).

Or, g.f.: [(1+(1-t)*z])*C/[(1+(1-t)*z*(1+z*C)]).

STATUS

proposed

editing

#10 by Michel Marcus at Tue Oct 27 05:12:36 EDT 2015

STATUS

editing

proposed

#9 by Michel Marcus at Tue Oct 27 05:12:29 EDT 2015

REFERENCES

A. Sapounakis, I. Tasoulas and P. Tsikouras, Counting strings in Dyck paths, Discrete Math., 307 (2007), 2909-2924.

LINKS

A. Sapounakis, I. Tasoulas and P. Tsikouras, <a href="http://dx.doi.org/10.1016/j.disc.2007.03.005">Counting strings in Dyck paths</a>, Discrete Math., 307 (2007), 2909-2924.

FORMULA

G.f.=: (1+z-tzt*z)/[1+z-tzt*z+z^2-tzt*z^2-zCz*C(1+z-tzt*z)], where C = [1-sqrt(1-4z4*z)]/(2z2*z) is the Catalan g.f. (see A000108).

Or, g.f.=: [1+(1-t)*z]*C/[1+(1-t)*z*(1+zCz*C)].

EXTENSIONS

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of _R. J. Mathar._

STATUS

approved

editing

#8 by Russ Cox at Fri Mar 30 17:36:12 EDT 2012

AUTHOR

_Emeric Deutsch (deutsch(AT)duke.poly.edu), _, Feb 27 2007

Discussion

Fri Mar 30

17:36

OEIS Server: https://oeis.org/edit/global/173

#7 by Russ Cox at Fri Mar 30 16:50:39 EDT 2012

EXTENSIONS

Edited by _N. J. A. Sloane (njas(AT)research.att.com), _, May 16 2008 at the suggestion of R. J. Mathar.

Discussion

Fri Mar 30

16:50

OEIS Server: https://oeis.org/edit/global/110

#6 by T. D. Noe at Mon Oct 10 13:11:16 EDT 2011

STATUS

proposed

approved

#5 by Tom Copeland at Sun Oct 09 17:33:46 EDT 2011

STATUS

editing

proposed