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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.

A182900 Triangle read by rows: T(n,k) is the number of weighted lattice paths in B(n) having k valleys. The members of B(n) are paths of weight n that start at (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A valley is a (1,-1)-step followed by a (1,1)-step.

Table of values

n a(n)
0 1
1 1
2 2
3 4
4 8
5 17
6 36
7 1
8 78
9 4
10 171
11 14
12 379
13 43
14 1
15 848
16 125
17 5
18 1912
19 351
20 20
21 4341
22 960
23 71
24 1
25 9915
26 2579
27 235
28 6
29 22767
30 6833
31 745
32 27
33 52526
34 17916
35 2281
36 108
37 1
38 121698
39 46593
40 6805
41 399
42 7
43 283043
44 120385
45 19885
46 1400
47 35
48 660579
49 309416
50 57141
51 4712
52 155
53 1

List of values

[1, 1, 2, 4, 8, 17, 36, 1, 78, 4, 171, 14, 379, 43, 1, 848, 125, 5, 1912, 351, 20, 4341, 960, 71, 1, 9915, 2579, 235, 6, 22767, 6833, 745, 27, 52526, 17916, 2281, 108, 1, 121698, 46593, 6805, 399, 7, 283043, 120385, 19885, 1400, 35, 660579, 309416, 57141, 4712, 155, 1]

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