A243828 - cp's OEIS frontend

A243828 Number A(n,k) of Dyck paths of semilength n having exactly two (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of k, where 1=U=(1,1) and 0=D=(1,-1); square array A(n,k), n>=0, k>=0, read by antidiagonals.

n	a(n)
0	0
1	0
2	0
3	0
4	0
5	2
6	0
7	0
8	2
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	0
18	3
19	0
20	0
21	0
22	0
23	0
24	1
25	6
26	0
27	0
28	0
29	0
30	0
31	0
32	6
33	10
34	0
35	0
36	0
37	0
38	0
39	1
40	2
41	20
42	15
43	0
44	0
45	0
46	0
47	0
48	0
49	3
50	15
51	50
52	21
53	0
54	0
55	0
56	0
57	0
58	0
59	2
60	12
61	69
62	105
63	28
64	0
65	0
66	0
67	0
68	0
69	0
70	1
71	15
72	40
73	252
74	196
75	36
76	0
77	0
78	0
79	0
80	0
81	0
82	0
83	5
84	69
85	135
86	804
87	336
88	45
89	0
90	0

[0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 6, 10, 0, 0, 0, 0, 0, 1, 2, 20, 15, 0, 0, 0, 0, 0, 0, 3, 15, 50, 21, 0, 0, 0, 0, 0, 0, 2, 12, 69, 105, 28, 0, 0, 0, 0, 0, 0, 1, 15, 40, 252, 196, 36, 0, 0, 0, 0, 0, 0, 0, 5, 69, 135, 804, 336, 45, 0, 0]

cp's OEIS Frontend

A243828 Number A(n,k) of Dyck paths of semilength n having exactly two (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of k, where 1=U=(1,1) and 0=D=(1,-1); square array A(n,k), n>=0, k>=0, read by antidiagonals.

Table of values

List of values

n	a(n)
0	0
1	0
2	0
3	0
4	0
5	2
6	0
7	0
8	2
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	0
18	3
19	0
20	0
21	0
22	0
23	0
24	1
25	6
26	0
27	0
28	0
29	0
30	0
31	0
32	6
33	10
34	0
35	0
36	0
37	0
38	0
39	1
40	2
41	20
42	15
43	0
44	0
45	0
46	0
47	0
48	0
49	3
50	15
51	50
52	21
53	0
54	0
55	0
56	0
57	0
58	0
59	2
60	12
61	69
62	105
63	28
64	0
65	0
66	0
67	0
68	0
69	0
70	1
71	15
72	40
73	252
74	196
75	36
76	0
77	0
78	0
79	0
80	0
81	0
82	0
83	5
84	69
85	135
86	804
87	336
88	45
89	0
90	0

n	a(n)
0	0
1	0
2	0
3	0
4	0
5	2
6	0
7	0
8	2
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	0
18	3
19	0
20	0
21	0
22	0
23	0
24	1
25	6
26	0
27	0
28	0
29	0
30	0
31	0
32	6
33	10
34	0
35	0
36	0
37	0
38	0
39	1
40	2
41	20
42	15
43	0
44	0
45	0
46	0
47	0
48	0
49	3
50	15
51	50
52	21
53	0
54	0
55	0
56	0
57	0
58	0
59	2
60	12
61	69
62	105
63	28
64	0
65	0
66	0
67	0
68	0
69	0
70	1
71	15
72	40
73	252
74	196
75	36
76	0
77	0
78	0
79	0
80	0
81	0
82	0
83	5
84	69
85	135
86	804
87	336
88	45
89	0
90	0

n	a(n)
0	0
1	0
2	0
3	0
4	0
5	2
6	0
7	0
8	2
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	0
18	3
19	0
20	0
21	0
22	0
23	0
24	1
25	6
26	0
27	0
28	0
29	0
30	0
31	0
32	6
33	10
34	0
35	0
36	0
37	0
38	0
39	1
40	2
41	20
42	15
43	0
44	0
45	0
46	0
47	0
48	0
49	3
50	15
51	50
52	21
53	0
54	0
55	0
56	0
57	0
58	0
59	2
60	12
61	69
62	105
63	28
64	0
65	0
66	0
67	0
68	0
69	0
70	1
71	15
72	40
73	252
74	196
75	36
76	0
77	0
78	0
79	0
80	0
81	0
82	0
83	5
84	69
85	135
86	804
87	336
88	45
89	0
90	0