A191312 - cp's OEIS frontend

A191312 Triangle read by rows: T(n,k) is the number of dispersed Dyck paths (i.e., Motzkin paths with no (1,0) steps at positive heights) of length n having abscissa of the first return to the horizontal axis equal to k (assumed to be 0 if there are no such returns).

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	1
9	1
10	1
11	0
12	2
13	1
14	2
15	1
16	0
17	3
18	2
19	2
20	2
21	1
22	0
23	6
24	3
25	4
26	2
27	4
28	1
29	0
30	10
31	6
32	6
33	4
34	4
35	4
36	1
37	0
38	20
39	10
40	12
41	6
42	8
43	4
44	9
45	1
46	0
47	35
48	20
49	20
50	12
51	12
52	8
53	9
54	9
55	1
56	0
57	70
58	35
59	40
60	20
61	24
62	12
63	18
64	9
65	23
66	1
67	0
68	126
69	70
70	70
71	40
72	40
73	24
74	27
75	18
76	23
77	23
78	1
79	0
80	252
81	126
82	140
83	70
84	80
85	40
86	54
87	27
88	46
89	23
90	65

[1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 0, 3, 2, 2, 2, 1, 0, 6, 3, 4, 2, 4, 1, 0, 10, 6, 6, 4, 4, 4, 1, 0, 20, 10, 12, 6, 8, 4, 9, 1, 0, 35, 20, 20, 12, 12, 8, 9, 9, 1, 0, 70, 35, 40, 20, 24, 12, 18, 9, 23, 1, 0, 126, 70, 70, 40, 40, 24, 27, 18, 23, 23, 1, 0, 252, 126, 140, 70, 80, 40, 54, 27, 46, 23, 65]

cp's OEIS Frontend

A191312 Triangle read by rows: T(n,k) is the number of dispersed Dyck paths (i.e., Motzkin paths with no (1,0) steps at positive heights) of length n having abscissa of the first return to the horizontal axis equal to k (assumed to be 0 if there are no such returns).

Table of values

List of values

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	1
9	1
10	1
11	0
12	2
13	1
14	2
15	1
16	0
17	3
18	2
19	2
20	2
21	1
22	0
23	6
24	3
25	4
26	2
27	4
28	1
29	0
30	10
31	6
32	6
33	4
34	4
35	4
36	1
37	0
38	20
39	10
40	12
41	6
42	8
43	4
44	9
45	1
46	0
47	35
48	20
49	20
50	12
51	12
52	8
53	9
54	9
55	1
56	0
57	70
58	35
59	40
60	20
61	24
62	12
63	18
64	9
65	23
66	1
67	0
68	126
69	70
70	70
71	40
72	40
73	24
74	27
75	18
76	23
77	23
78	1
79	0
80	252
81	126
82	140
83	70
84	80
85	40
86	54
87	27
88	46
89	23
90	65

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	1
9	1
10	1
11	0
12	2
13	1
14	2
15	1
16	0
17	3
18	2
19	2
20	2
21	1
22	0
23	6
24	3
25	4
26	2
27	4
28	1
29	0
30	10
31	6
32	6
33	4
34	4
35	4
36	1
37	0
38	20
39	10
40	12
41	6
42	8
43	4
44	9
45	1
46	0
47	35
48	20
49	20
50	12
51	12
52	8
53	9
54	9
55	1
56	0
57	70
58	35
59	40
60	20
61	24
62	12
63	18
64	9
65	23
66	1
67	0
68	126
69	70
70	70
71	40
72	40
73	24
74	27
75	18
76	23
77	23
78	1
79	0
80	252
81	126
82	140
83	70
84	80
85	40
86	54
87	27
88	46
89	23
90	65

n	a(n)
0	1
1	1
2	0
3	1
4	0
5	1
6	1
7	0
8	1
9	1
10	1
11	0
12	2
13	1
14	2
15	1
16	0
17	3
18	2
19	2
20	2
21	1
22	0
23	6
24	3
25	4
26	2
27	4
28	1
29	0
30	10
31	6
32	6
33	4
34	4
35	4
36	1
37	0
38	20
39	10
40	12
41	6
42	8
43	4
44	9
45	1
46	0
47	35
48	20
49	20
50	12
51	12
52	8
53	9
54	9
55	1
56	0
57	70
58	35
59	40
60	20
61	24
62	12
63	18
64	9
65	23
66	1
67	0
68	126
69	70
70	70
71	40
72	40
73	24
74	27
75	18
76	23
77	23
78	1
79	0
80	252
81	126
82	140
83	70
84	80
85	40
86	54
87	27
88	46
89	23
90	65