The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A008315

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A008315

Catalan triangle read by rows. Also triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
(history; published version)

#110 by Michel Marcus at Sat Aug 03 16:39:09 EDT 2024

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#109 by Andrew Howroyd at Sat Aug 03 16:37:49 EDT 2024

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#108 by Jason Yuen at Sat Aug 03 16:30:35 EDT 2024

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#107 by Jason Yuen at Sat Aug 03 16:30:31 EDT 2024

COMMENTS

T(n,k) is the number of dispersed Dyck paths (i.e. Motzkin paths with no (1,0) steps at positive heights) of length n and having k (1,1)-steps. Example: T(5,1)=4 because, denoting U=(1,1), D=(1,-1), H=(1,0), we have HHHUD, HHUDH, HUDHH, and UDHHH. - Emeric Deutsch, May 30 2011

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editing

#106 by Michael De Vlieger at Fri Jul 05 11:10:55 EDT 2024

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reviewed

approved

#105 by Michel Marcus at Fri Jul 05 10:50:39 EDT 2024

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proposed

reviewed

#104 by Michael De Vlieger at Fri Jul 05 10:44:16 EDT 2024

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#103 by Michael De Vlieger at Fri Jul 05 10:44:14 EDT 2024

LINKS

Chassidy Bozeman, Christine Cheng, Pamela E. Harris, Stephen Lasinis, and Shanise Walker, <a href="https://arxiv.org/abs/2406.19562">The Pinnacle Sets of a Graph</a>, arXiv:2406.19562 [math.CO], 2024. See pp. 9-10.

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approved

editing

#102 by Alois P. Heinz at Fri Oct 14 16:19:03 EDT 2022

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approved

#101 by Alois P. Heinz at Fri Oct 14 16:18:57 EDT 2022

FORMULA

Sum_{k, =0<=k<=..n} T(n,k)*x^k = A000012(n), A001405(n), A126087(n), A128386(n), A121724(n), A128387(n), A132373(n), A132374(n), A132375(n), A121725(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively. - Philippe Deléham, Dec 12 2011

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approved

editing