A162981 - cp's OEIS frontend

A162981 Number of Dyck paths with no UUU's and no DDD's of semilength n and having k returns to the x-axis (1 <= k <= n; U=(1,1), D=(1,-1)).

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	2
12	4
13	6
14	4
15	1
16	4
17	7
18	10
19	10
20	5
21	1
22	8
23	14
24	18
25	20
26	15
27	6
28	1
29	17
30	29
31	36
32	39
33	35
34	21
35	7
36	1
37	37
38	62
39	76
40	80
41	75
42	56
43	28
44	8
45	1
46	82
47	136
48	165
49	172
50	161
51	132
52	84
53	36
54	9
55	1
56	185
57	304
58	366
59	380
60	355
61	300
62	217
63	120
64	45
65	10
66	1
67	423
68	690
69	826
70	855
71	800
72	684
73	525

[1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 4, 6, 4, 1, 4, 7, 10, 10, 5, 1, 8, 14, 18, 20, 15, 6, 1, 17, 29, 36, 39, 35, 21, 7, 1, 37, 62, 76, 80, 75, 56, 28, 8, 1, 82, 136, 165, 172, 161, 132, 84, 36, 9, 1, 185, 304, 366, 380, 355, 300, 217, 120, 45, 10, 1, 423, 690, 826, 855, 800, 684, 525]

cp's OEIS Frontend

A162981 Number of Dyck paths with no UUU's and no DDD's of semilength n and having k returns to the x-axis (1 <= k <= n; U=(1,1), D=(1,-1)).

Table of values

List of values

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	2
12	4
13	6
14	4
15	1
16	4
17	7
18	10
19	10
20	5
21	1
22	8
23	14
24	18
25	20
26	15
27	6
28	1
29	17
30	29
31	36
32	39
33	35
34	21
35	7
36	1
37	37
38	62
39	76
40	80
41	75
42	56
43	28
44	8
45	1
46	82
47	136
48	165
49	172
50	161
51	132
52	84
53	36
54	9
55	1
56	185
57	304
58	366
59	380
60	355
61	300
62	217
63	120
64	45
65	10
66	1
67	423
68	690
69	826
70	855
71	800
72	684
73	525

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	2
12	4
13	6
14	4
15	1
16	4
17	7
18	10
19	10
20	5
21	1
22	8
23	14
24	18
25	20
26	15
27	6
28	1
29	17
30	29
31	36
32	39
33	35
34	21
35	7
36	1
37	37
38	62
39	76
40	80
41	75
42	56
43	28
44	8
45	1
46	82
47	136
48	165
49	172
50	161
51	132
52	84
53	36
54	9
55	1
56	185
57	304
58	366
59	380
60	355
61	300
62	217
63	120
64	45
65	10
66	1
67	423
68	690
69	826
70	855
71	800
72	684
73	525

n	a(n)
1	1
2	1
3	1
4	1
5	2
6	1
7	1
8	3
9	3
10	1
11	2
12	4
13	6
14	4
15	1
16	4
17	7
18	10
19	10
20	5
21	1
22	8
23	14
24	18
25	20
26	15
27	6
28	1
29	17
30	29
31	36
32	39
33	35
34	21
35	7
36	1
37	37
38	62
39	76
40	80
41	75
42	56
43	28
44	8
45	1
46	82
47	136
48	165
49	172
50	161
51	132
52	84
53	36
54	9
55	1
56	185
57	304
58	366
59	380
60	355
61	300
62	217
63	120
64	45
65	10
66	1
67	423
68	690
69	826
70	855
71	800
72	684
73	525