A246179 - cp's OEIS frontend

A246179 Triangle read by rows: T(n,k) is the number of weighted lattice paths in B(n) having k returns to the horizontal axis (i.e., (1,-1)-steps ending on the horizontal axis). The members of B(n) are paths of weight n that start in (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: a (1,0)-step with weight 1; a (1,0)-step with weight 2; a (1,1)-step with weight 2; a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.

n	a(n)
0	1
1	1
2	2
3	3
4	1
5	5
6	3
7	8
8	9
9	13
10	23
11	1
12	21
13	56
14	5
15	34
16	131
17	20
18	55
19	300
20	67
21	1
22	89
23	678
24	204
25	7
26	144
27	1523
28	581
29	35
30	233
31	3416
32	1580
33	143
34	1
35	377
36	7677
37	4155
38	517
39	9
40	610
41	17329
42	10663
43	1716
44	54
45	987
46	39353
47	26880
48	5352
49	259
50	1
51	1597
52	90000
53	66891
54	15924
55	1079

[1, 1, 2, 3, 1, 5, 3, 8, 9, 13, 23, 1, 21, 56, 5, 34, 131, 20, 55, 300, 67, 1, 89, 678, 204, 7, 144, 1523, 581, 35, 233, 3416, 1580, 143, 1, 377, 7677, 4155, 517, 9, 610, 17329, 10663, 1716, 54, 987, 39353, 26880, 5352, 259, 1, 1597, 90000, 66891, 15924, 1079]

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