A217540 - cp's OEIS frontend

A217540 Scambler statistic on Dyck paths. Triangle T(n, k) read by rows, n >= 0, -n <= k <= n, T(n, k) is the number of Dyck paths of semilength n and k = number of returns + number of hills - number of peaks.

n	a(n)
0	1
1	0
2	0
3	1
4	0
5	0
6	1
7	0
8	1
9	0
10	0
11	1
12	1
13	2
14	0
15	1
16	0
17	0
18	1
19	3
20	4
21	2
22	3
23	0
24	1
25	0
26	0
27	1
28	6
29	10
30	9
31	8
32	3
33	4
34	0
35	1
36	0
37	0
38	1
39	10
40	25
41	30
42	26
43	17
44	13
45	4
46	5
47	0
48	1
49	0
50	0
51	1
52	15
53	56
54	90
55	90
56	70
57	49
58	27
59	19
60	5
61	6
62	0
63	1
64	0
65	0
66	1
67	21
68	112
69	245
70	301
71	266
72	197
73	128
74	80
75	39
76	26
77	6
78	7
79	0
80	1

[1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 3, 4, 2, 3, 0, 1, 0, 0, 1, 6, 10, 9, 8, 3, 4, 0, 1, 0, 0, 1, 10, 25, 30, 26, 17, 13, 4, 5, 0, 1, 0, 0, 1, 15, 56, 90, 90, 70, 49, 27, 19, 5, 6, 0, 1, 0, 0, 1, 21, 112, 245, 301, 266, 197, 128, 80, 39, 26, 6, 7, 0, 1]

cp's OEIS Frontend

A217540 Scambler statistic on Dyck paths. Triangle T(n, k) read by rows, n >= 0, -n <= k <= n, T(n, k) is the number of Dyck paths of semilength n and k = number of returns + number of hills - number of peaks.

Table of values

List of values

n	a(n)
0	1
1	0
2	0
3	1
4	0
5	0
6	1
7	0
8	1
9	0
10	0
11	1
12	1
13	2
14	0
15	1
16	0
17	0
18	1
19	3
20	4
21	2
22	3
23	0
24	1
25	0
26	0
27	1
28	6
29	10
30	9
31	8
32	3
33	4
34	0
35	1
36	0
37	0
38	1
39	10
40	25
41	30
42	26
43	17
44	13
45	4
46	5
47	0
48	1
49	0
50	0
51	1
52	15
53	56
54	90
55	90
56	70
57	49
58	27
59	19
60	5
61	6
62	0
63	1
64	0
65	0
66	1
67	21
68	112
69	245
70	301
71	266
72	197
73	128
74	80
75	39
76	26
77	6
78	7
79	0
80	1

n	a(n)
0	1
1	0
2	0
3	1
4	0
5	0
6	1
7	0
8	1
9	0
10	0
11	1
12	1
13	2
14	0
15	1
16	0
17	0
18	1
19	3
20	4
21	2
22	3
23	0
24	1
25	0
26	0
27	1
28	6
29	10
30	9
31	8
32	3
33	4
34	0
35	1
36	0
37	0
38	1
39	10
40	25
41	30
42	26
43	17
44	13
45	4
46	5
47	0
48	1
49	0
50	0
51	1
52	15
53	56
54	90
55	90
56	70
57	49
58	27
59	19
60	5
61	6
62	0
63	1
64	0
65	0
66	1
67	21
68	112
69	245
70	301
71	266
72	197
73	128
74	80
75	39
76	26
77	6
78	7
79	0
80	1

n	a(n)
0	1
1	0
2	0
3	1
4	0
5	0
6	1
7	0
8	1
9	0
10	0
11	1
12	1
13	2
14	0
15	1
16	0
17	0
18	1
19	3
20	4
21	2
22	3
23	0
24	1
25	0
26	0
27	1
28	6
29	10
30	9
31	8
32	3
33	4
34	0
35	1
36	0
37	0
38	1
39	10
40	25
41	30
42	26
43	17
44	13
45	4
46	5
47	0
48	1
49	0
50	0
51	1
52	15
53	56
54	90
55	90
56	70
57	49
58	27
59	19
60	5
61	6
62	0
63	1
64	0
65	0
66	1
67	21
68	112
69	245
70	301
71	266
72	197
73	128
74	80
75	39
76	26
77	6
78	7
79	0
80	1