A140717 - cp's OEIS frontend

A140717 Triangle read by rows: T(n,k) is the number of Dyck paths d of semilength n such that sum of peakheights of d - number of peaks of d = k (n >= 0, 0 <= k <= floor(n^2/4)).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	2
7	1
8	3
9	5
10	4
11	1
12	1
13	4
14	9
15	12
16	10
17	4
18	2
19	1
20	5
21	14
22	25
23	31
24	26
25	16
26	9
27	4
28	1
29	1
30	6
31	20
32	44
33	70
34	82
35	74
36	54
37	38
38	22
39	12
40	4
41	2
42	1
43	7
44	27
45	70
46	134
47	196
48	227
49	215
50	179
51	139
52	99
53	64
54	38
55	20
56	9
57	4
58	1
59	1
60	8
61	35
62	104
63	231
64	400
65	558
66	644
67	641
68	576
69	488
70	384
71	288
72	200
73	134
74	80

[1, 1, 1, 1, 1, 2, 2, 1, 3, 5, 4, 1, 1, 4, 9, 12, 10, 4, 2, 1, 5, 14, 25, 31, 26, 16, 9, 4, 1, 1, 6, 20, 44, 70, 82, 74, 54, 38, 22, 12, 4, 2, 1, 7, 27, 70, 134, 196, 227, 215, 179, 139, 99, 64, 38, 20, 9, 4, 1, 1, 8, 35, 104, 231, 400, 558, 644, 641, 576, 488, 384, 288, 200, 134, 80]

cp's OEIS Frontend

A140717 Triangle read by rows: T(n,k) is the number of Dyck paths d of semilength n such that sum of peakheights of d - number of peaks of d = k (n >= 0, 0 <= k <= floor(n^2/4)).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	2
7	1
8	3
9	5
10	4
11	1
12	1
13	4
14	9
15	12
16	10
17	4
18	2
19	1
20	5
21	14
22	25
23	31
24	26
25	16
26	9
27	4
28	1
29	1
30	6
31	20
32	44
33	70
34	82
35	74
36	54
37	38
38	22
39	12
40	4
41	2
42	1
43	7
44	27
45	70
46	134
47	196
48	227
49	215
50	179
51	139
52	99
53	64
54	38
55	20
56	9
57	4
58	1
59	1
60	8
61	35
62	104
63	231
64	400
65	558
66	644
67	641
68	576
69	488
70	384
71	288
72	200
73	134
74	80

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	2
7	1
8	3
9	5
10	4
11	1
12	1
13	4
14	9
15	12
16	10
17	4
18	2
19	1
20	5
21	14
22	25
23	31
24	26
25	16
26	9
27	4
28	1
29	1
30	6
31	20
32	44
33	70
34	82
35	74
36	54
37	38
38	22
39	12
40	4
41	2
42	1
43	7
44	27
45	70
46	134
47	196
48	227
49	215
50	179
51	139
52	99
53	64
54	38
55	20
56	9
57	4
58	1
59	1
60	8
61	35
62	104
63	231
64	400
65	558
66	644
67	641
68	576
69	488
70	384
71	288
72	200
73	134
74	80

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	2
6	2
7	1
8	3
9	5
10	4
11	1
12	1
13	4
14	9
15	12
16	10
17	4
18	2
19	1
20	5
21	14
22	25
23	31
24	26
25	16
26	9
27	4
28	1
29	1
30	6
31	20
32	44
33	70
34	82
35	74
36	54
37	38
38	22
39	12
40	4
41	2
42	1
43	7
44	27
45	70
46	134
47	196
48	227
49	215
50	179
51	139
52	99
53	64
54	38
55	20
56	9
57	4
58	1
59	1
60	8
61	35
62	104
63	231
64	400
65	558
66	644
67	641
68	576
69	488
70	384
71	288
72	200
73	134
74	80