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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A371408 Number of Dyck paths of semilength n having exactly three (possibly overlapping) occurrences of the consecutive step pattern UDU, where U = (1,1) and D = (1,-1).

Table of values

n a(n)
0 0
1 0
2 0
3 0
4 1
5 4
6 20
7 80
8 315
9 1176
10 4284
11 15240
12 53295
13 183700
14 625768
15 2110472
16 7057505
17 23427600
18 77271120
19 253426752
20 827009523
21 2686728060
22 8693388060
23 28026897360
24 90058925649
25 288516259416
26 921755412900
27 2937377079000
28 9338728806225
29 29626186593276

List of values

[0, 0, 0, 0, 1, 4, 20, 80, 315, 1176, 4284, 15240, 53295, 183700, 625768, 2110472, 7057505, 23427600, 77271120, 253426752, 827009523, 2686728060, 8693388060, 28026897360, 90058925649, 288516259416, 921755412900, 2937377079000, 9338728806225, 29626186593276]

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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