A129183 - cp's OEIS frontend

A129183 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n such that the sum of the height of the peaks is k (n>=0; n<=k<=floor((n+1)^2/4)).

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	2
6	0
7	0
8	0
9	4
10	1
11	0
12	0
13	0
14	0
15	8
16	4
17	2
18	0
19	0
20	0
21	0
22	0
23	16
24	12
25	9
26	4
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	32
35	32
36	30
37	20
38	12
39	4
40	2
41	0
42	0
43	0
44	0
45	0
46	0
47	0
48	64
49	80
50	88
51	73
52	56
53	34
54	20
55	9
56	4
57	1
58	0
59	0
60	0
61	0
62	0
63	0
64	0
65	0
66	128
67	192
68	240
69	232
70	206
71	156
72	116
73	72
74	46
75	24
76	12
77	4
78	2
79	0
80	0
81	0
82	0
83	0
84	0
85	0
86	0
87	0

[1, 0, 1, 0, 0, 2, 0, 0, 0, 4, 1, 0, 0, 0, 0, 8, 4, 2, 0, 0, 0, 0, 0, 16, 12, 9, 4, 1, 0, 0, 0, 0, 0, 0, 32, 32, 30, 20, 12, 4, 2, 0, 0, 0, 0, 0, 0, 0, 64, 80, 88, 73, 56, 34, 20, 9, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 128, 192, 240, 232, 206, 156, 116, 72, 46, 24, 12, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]

cp's OEIS Frontend

A129183 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n such that the sum of the height of the peaks is k (n>=0; n<=k<=floor((n+1)^2/4)).

Table of values

List of values

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	2
6	0
7	0
8	0
9	4
10	1
11	0
12	0
13	0
14	0
15	8
16	4
17	2
18	0
19	0
20	0
21	0
22	0
23	16
24	12
25	9
26	4
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	32
35	32
36	30
37	20
38	12
39	4
40	2
41	0
42	0
43	0
44	0
45	0
46	0
47	0
48	64
49	80
50	88
51	73
52	56
53	34
54	20
55	9
56	4
57	1
58	0
59	0
60	0
61	0
62	0
63	0
64	0
65	0
66	128
67	192
68	240
69	232
70	206
71	156
72	116
73	72
74	46
75	24
76	12
77	4
78	2
79	0
80	0
81	0
82	0
83	0
84	0
85	0
86	0
87	0

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	2
6	0
7	0
8	0
9	4
10	1
11	0
12	0
13	0
14	0
15	8
16	4
17	2
18	0
19	0
20	0
21	0
22	0
23	16
24	12
25	9
26	4
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	32
35	32
36	30
37	20
38	12
39	4
40	2
41	0
42	0
43	0
44	0
45	0
46	0
47	0
48	64
49	80
50	88
51	73
52	56
53	34
54	20
55	9
56	4
57	1
58	0
59	0
60	0
61	0
62	0
63	0
64	0
65	0
66	128
67	192
68	240
69	232
70	206
71	156
72	116
73	72
74	46
75	24
76	12
77	4
78	2
79	0
80	0
81	0
82	0
83	0
84	0
85	0
86	0
87	0

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	2
6	0
7	0
8	0
9	4
10	1
11	0
12	0
13	0
14	0
15	8
16	4
17	2
18	0
19	0
20	0
21	0
22	0
23	16
24	12
25	9
26	4
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	32
35	32
36	30
37	20
38	12
39	4
40	2
41	0
42	0
43	0
44	0
45	0
46	0
47	0
48	64
49	80
50	88
51	73
52	56
53	34
54	20
55	9
56	4
57	1
58	0
59	0
60	0
61	0
62	0
63	0
64	0
65	0
66	128
67	192
68	240
69	232
70	206
71	156
72	116
73	72
74	46
75	24
76	12
77	4
78	2
79	0
80	0
81	0
82	0
83	0
84	0
85	0
86	0
87	0