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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.

A182901 Number of weighted lattice paths in B(n) having no 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 78
8 171
9 379
10 848
11 1912
12 4341
13 9915
14 22767
15 52526
16 121698
17 283043
18 660579
19 1546556
20 3631261
21 8548643
22 20174093
23 47716388
24 113095740
25 268575321
26 638954183
27 1522668500
28 3634346039
29 8687404327
30 20794957839
31 49841956726
32 119610395745

List of values

[1, 1, 2, 4, 8, 17, 36, 78, 171, 379, 848, 1912, 4341, 9915, 22767, 52526, 121698, 283043, 660579, 1546556, 3631261, 8548643, 20174093, 47716388, 113095740, 268575321, 638954183, 1522668500, 3634346039, 8687404327, 20794957839, 49841956726, 119610395745]

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

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