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Revision History for A059231 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
A059231 Number of different lattice paths running from (0,0) to (n,0) using steps from S = {(k,k) or (k,-k): k positive integer} that never go below the x-axis.
(history; published version)
#111 by Peter Luschny at Tue Sep 17 13:29:24 EDT 2024
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reviewed

approved

#110 by Michel Marcus at Tue Sep 17 12:43:33 EDT 2024
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proposed

reviewed

#109 by Michael De Vlieger at Tue Sep 17 09:48:08 EDT 2024
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editing

proposed

#108 by Michael De Vlieger at Tue Sep 17 09:47:56 EDT 2024
LINKS

Z. Zhi Chen, H. and Hao Pan, <a href="httphttps://arxiv.org/abs/1608.02448">Identities involving weighted Catalan-, Schroder and Motzkin Pathspaths</a>, arXiv:1608.02448 [math.CO], (2016), . See eq. (1.13), a=1, b=4.

C. Curtis Coker, <a href="http://dx.doi.org/10.1016/S0012-365X(03)00037-2">Enumerating a class of lattice paths</a>, Discrete Math., 271 (2003), 13-28 (the sequence d_n).

C. Curtis Coker, <a href="http://dx.doi.org/10.1016/j.disc.2003.12.008">A family of eigensequences</a>, Discrete Math. 282 (2004), 249-250.

J. Joseph P. S. Kung and A. Anna de Mier, <a href="http://dx.doi.org/10.1016/j.jcta.2012.08.010">Catalan lattice paths with rook, bishop and spider steps</a>, Journal of Combinatorial Theory, J. Comb. Theor., Series A 120 (2013) Vol. 120, Issue 2, 379-389.

G. LGregory J. Morrow, <a href="httphttps://dx.doi.org/10.1016/j.spa.2014.12.005">Laws relating runs and steps in gambler's ruin</a>, Stochastic Processes and their Applications, Proc. Appl. (2024) Vol. 125 (2015) , Issue 5, 2010-2025.

W.Wen-j. jin Woan, <a href="https://zbmath.org/?q=an:01735667">Diagonal lattice paths</a>, Congr. Numer. 151 (2001) 173-178

#107 by Michael De Vlieger at Tue Sep 17 09:44:22 EDT 2024
LINKS

Greg Morrow, <a href="https://faculty.uccs.edu/gmorrow/wp-content/uploads/sites/19/2024/08/Prob_Distrns__Int_Seqs_related_to_Rook_Paths_Aug_9_2024.pdf">Some probability distributions and integer sequences related to rook paths</a>, Univ. Colorado Springs (2024). See pp. 1, 4, 15, 22.

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approved

editing

#106 by Amiram Eldar at Fri Jul 14 04:13:37 EDT 2023
STATUS

editing

approved

#105 by Amiram Eldar at Fri Jul 14 04:13:34 EDT 2023
LINKS

Paul Barry and Aoife Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Barry2/barry126.html">A Note on Narayana Triangles and Related Polynomials, Riordan Arrays, and MIMO Capacity Calculations</a>, J. Int. Seq. 14 (2011) # , Article 11.3.8.

Paul Barry and Aoife Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Barry2/barry190r.html">Generalized Narayana Polynomials, Riordan Arrays, and Lattice Paths</a>, Journal of Integer Sequences, Vol. 15, (2012, #), Article 12.4.8.

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reviewed

editing

#104 by Joerg Arndt at Fri Jul 14 01:38:53 EDT 2023
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proposed

reviewed

#103 by Michel Marcus at Fri Jul 14 01:29:12 EDT 2023
STATUS

editing

proposed

#102 by Michel Marcus at Fri Jul 14 01:29:06 EDT 2023
LINKS

P. Paul Barry, A. and Aoife Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Barry2/barry126.html">A Note on Narayana Triangles and Related Polynomials, Riordan Arrays, and MIMO Capacity Calculations </a>, J. Int. Seq. 14 (2011) # 11.3.8.

STATUS

approved

editing

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Last modified September 19 05:12 EDT 2024. Contains 376004 sequences. (Running on oeis4.)