The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A318942

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A318942

Triangle read by rows: T(n,k) = number of Dyck paths with n nodes and altitude k (1 <= k <= n).
(history; published version)

#27 by Peter Luschny at Sun Sep 25 11:28:35 EDT 2022

STATUS

reviewed

approved

#26 by Joerg Arndt at Sun Sep 25 11:15:23 EDT 2022

STATUS

proposed

reviewed

#25 by Jean-François Alcover at Sun Sep 25 08:07:23 EDT 2022

STATUS

editing

proposed

#24 by Jean-François Alcover at Sun Sep 25 08:07:11 EDT 2022

MATHEMATICA

T[n_, k_] := T[n, k] = Which[k == 1, Fibonacci[2*n - 1], n == k, 1, n == k + 1, 2*T[n - 1, k] + T[n - 1, k - 1], n >= k + 2, 2*T[n - 1, k] + T[n - 1, k - 1] - T[n - 2, k - 1] + Fibonacci[2*n - 2*k - 2], True, 0];

Table[Table[T[n, k], {k, 1, n}], {n, 1, 12}] // Flatten (* Jean-François Alcover, Sep 25 2022, after R. J. Mathar *)

STATUS

approved

editing

#23 by Alois P. Heinz at Thu Apr 11 11:46:45 EDT 2019

STATUS

editing

approved

#22 by Alois P. Heinz at Thu Apr 11 11:32:04 EDT 2019

MAPLE

option remember;

Discussion

Thu Apr 11

11:32

Alois P. Heinz: option remember; for efficiency needed!

#21 by Alois P. Heinz at Thu Apr 11 11:30:34 EDT 2019

CROSSREFS

ow Row sums give A038731(n-1).

#20 by Alois P. Heinz at Thu Apr 11 11:30:06 EDT 2019

CROSSREFS

ow sums give A038731(n-1).

STATUS

approved

editing

#19 by R. J. Mathar at Tue Apr 09 10:33:39 EDT 2019

STATUS

editing

approved

#18 by R. J. Mathar at Tue Apr 09 10:33:03 EDT 2019

LINKS

Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L. (2018). <a href="https://doi.org/10.1016/j.disc.2018.01606.032">Enumerations of peaks and valleys on non-decreasing Dyck paths</a>. Discrete Mathematics, 341(10), 2789-2807.