A109194 - cp's OEIS frontend

A109194 Number of returns to the x-axis (i.e., d or u steps hitting the x-axis) in all Grand Motzkin paths of length n. (A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).

n	a(n)
2	2
3	6
4	22
5	70
6	224
7	700
8	2174
9	6702
10	20572
11	62920
12	191932
13	584220
14	1775258
15	5386846
16	16326734
17	49435150
18	149557436
19	452133880
20	1366012832
21	4124825872
22	12449394278
23	37558361290
24	113266431860
25	341467468420
26	1029119688014

[2, 6, 22, 70, 224, 700, 2174, 6702, 20572, 62920, 191932, 584220, 1775258, 5386846, 16326734, 49435150, 149557436, 452133880, 1366012832, 4124825872, 12449394278, 37558361290, 113266431860, 341467468420, 1029119688014]

cp's OEIS Frontend

A109194 Number of returns to the x-axis (i.e., d or u steps hitting the x-axis) in all Grand Motzkin paths of length n. (A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).

Table of values

List of values