A145884 - cp's OEIS frontend

A145884 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n such that the difference between the sum of the valley abscissae and number of valleys is k (0 <= k <= (n-1)^2).

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	1
8	1
9	1
10	1
11	1
12	2
13	2
14	2
15	2
16	1
17	1
18	1
19	1
20	1
21	1
22	2
23	3
24	3
25	4
26	4
27	4
28	4
29	4
30	3
31	3
32	2
33	1
34	1
35	1
36	1
37	1
38	1
39	2
40	3
41	4
42	5
43	6
44	7
45	8
46	9
47	9
48	10
49	10
50	9
51	9
52	8
53	7
54	6
55	5
56	4
57	3
58	2
59	1
60	1
61	1
62	1
63	1
64	1
65	2
66	3
67	4
68	6
69	7
70	9
71	11
72	13
73	15
74	18
75	19
76	21
77	23
78	24
79	24
80	25
81	24
82	24
83	23
84	21
85	19
86	18
87	15
88	13
89	11
90	9
91	7
92	6
93	4
94	3

[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 4, 4, 3, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10, 10, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 15, 18, 19, 21, 23, 24, 24, 25, 24, 24, 23, 21, 19, 18, 15, 13, 11, 9, 7, 6, 4, 3]

cp's OEIS Frontend

A145884 Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n such that the difference between the sum of the valley abscissae and number of valleys is k (0 <= k <= (n-1)^2).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	1
8	1
9	1
10	1
11	1
12	2
13	2
14	2
15	2
16	1
17	1
18	1
19	1
20	1
21	1
22	2
23	3
24	3
25	4
26	4
27	4
28	4
29	4
30	3
31	3
32	2
33	1
34	1
35	1
36	1
37	1
38	1
39	2
40	3
41	4
42	5
43	6
44	7
45	8
46	9
47	9
48	10
49	10
50	9
51	9
52	8
53	7
54	6
55	5
56	4
57	3
58	2
59	1
60	1
61	1
62	1
63	1
64	1
65	2
66	3
67	4
68	6
69	7
70	9
71	11
72	13
73	15
74	18
75	19
76	21
77	23
78	24
79	24
80	25
81	24
82	24
83	23
84	21
85	19
86	18
87	15
88	13
89	11
90	9
91	7
92	6
93	4
94	3

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	1
8	1
9	1
10	1
11	1
12	2
13	2
14	2
15	2
16	1
17	1
18	1
19	1
20	1
21	1
22	2
23	3
24	3
25	4
26	4
27	4
28	4
29	4
30	3
31	3
32	2
33	1
34	1
35	1
36	1
37	1
38	1
39	2
40	3
41	4
42	5
43	6
44	7
45	8
46	9
47	9
48	10
49	10
50	9
51	9
52	8
53	7
54	6
55	5
56	4
57	3
58	2
59	1
60	1
61	1
62	1
63	1
64	1
65	2
66	3
67	4
68	6
69	7
70	9
71	11
72	13
73	15
74	18
75	19
76	21
77	23
78	24
79	24
80	25
81	24
82	24
83	23
84	21
85	19
86	18
87	15
88	13
89	11
90	9
91	7
92	6
93	4
94	3

n	a(n)
0	1
1	1
2	1
3	1
4	1
5	1
6	1
7	1
8	1
9	1
10	1
11	1
12	2
13	2
14	2
15	2
16	1
17	1
18	1
19	1
20	1
21	1
22	2
23	3
24	3
25	4
26	4
27	4
28	4
29	4
30	3
31	3
32	2
33	1
34	1
35	1
36	1
37	1
38	1
39	2
40	3
41	4
42	5
43	6
44	7
45	8
46	9
47	9
48	10
49	10
50	9
51	9
52	8
53	7
54	6
55	5
56	4
57	3
58	2
59	1
60	1
61	1
62	1
63	1
64	1
65	2
66	3
67	4
68	6
69	7
70	9
71	11
72	13
73	15
74	18
75	19
76	21
77	23
78	24
79	24
80	25
81	24
82	24
83	23
84	21
85	19
86	18
87	15
88	13
89	11
90	9
91	7
92	6
93	4
94	3