A253938 - cp's OEIS frontend

A253938 A pyramid F(n,p,r) of successive triangular arrays read by rows, relating Dyck path peaks and returns to the x axis (n = semilength of Dyck paths, p = number of peaks, r = returns to the x axis).

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

[1, 1, 0, 1, 1, 1, 2, 0, 0, 1, 1, 3, 3, 1, 2, 3, 0, 0, 0, 1, 1, 6, 4, 6, 8, 6, 1, 2, 3, 4, 0, 0, 0, 0, 1, 1, 10, 5, 20, 20, 10, 10, 15, 15, 10, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 1, 1, 15, 6, 50, 40, 15, 50, 60, 45, 20, 15, 24, 27, 24, 15, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0, 0, 1]

cp's OEIS Frontend

A253938 A pyramid F(n,p,r) of successive triangular arrays read by rows, relating Dyck path peaks and returns to the x axis (n = semilength of Dyck paths, p = number of peaks, r = returns to the x axis).

Table of values

List of values

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

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

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