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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.

A182897 Number of (1,-1)-returns to the horizontal axis in all weighted lattice paths in L_n. The members of L_n are paths of weight n that start at (0,0) , end on 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.

Table of values

n a(n)
0 0
1 0
2 0
3 1
4 3
5 9
6 27
7 76
8 211
9 580
10 1578
11 4267
12 11484
13 30789
14 82301
15 219465
16 584060
17 1551770
18 4117061
19 10910049
20 28881387
21 76387179
22 201875129
23 533145603
24 1407161007
25 3711981168
26 9787157469
27 25793933410
28 67952779665
29 178954077522

List of values

[0, 0, 0, 1, 3, 9, 27, 76, 211, 580, 1578, 4267, 11484, 30789, 82301, 219465, 584060, 1551770, 4117061, 10910049, 28881387, 76387179, 201875129, 533145603, 1407161007, 3711981168, 9787157469, 25793933410, 67952779665, 178954077522]

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

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