A243827 - cp's OEIS frontend

A243827 Number A(n,k) of Dyck paths of semilength n having exactly one occurrence 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	1
3	0
4	1
5	0
6	0
7	1
8	0
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	1
18	1
19	0
20	0
21	0
22	0
23	1
24	3
25	1
26	0
27	0
28	0
29	0
30	1
31	4
32	6
33	1
34	0
35	0
36	0
37	0
38	1
39	2
40	11
41	10
42	1
43	0
44	0
45	0
46	0
47	0
48	4
49	6
50	26
51	15
52	1
53	0
54	0
55	0
56	0
57	0
58	1
59	11
60	16
61	57
62	21
63	1
64	0
65	0
66	0
67	0
68	0
69	1
70	4
71	26
72	45
73	120
74	28
75	1
76	0
77	0
78	0
79	0
80	1
81	1
82	5
83	15
84	57
85	126
86	247
87	36
88	1
89	0
90	0

[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 4, 6, 1, 0, 0, 0, 0, 1, 2, 11, 10, 1, 0, 0, 0, 0, 0, 4, 6, 26, 15, 1, 0, 0, 0, 0, 0, 1, 11, 16, 57, 21, 1, 0, 0, 0, 0, 0, 1, 4, 26, 45, 120, 28, 1, 0, 0, 0, 0, 1, 1, 5, 15, 57, 126, 247, 36, 1, 0, 0]

cp's OEIS Frontend

A243827 Number A(n,k) of Dyck paths of semilength n having exactly one occurrence 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	1
3	0
4	1
5	0
6	0
7	1
8	0
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	1
18	1
19	0
20	0
21	0
22	0
23	1
24	3
25	1
26	0
27	0
28	0
29	0
30	1
31	4
32	6
33	1
34	0
35	0
36	0
37	0
38	1
39	2
40	11
41	10
42	1
43	0
44	0
45	0
46	0
47	0
48	4
49	6
50	26
51	15
52	1
53	0
54	0
55	0
56	0
57	0
58	1
59	11
60	16
61	57
62	21
63	1
64	0
65	0
66	0
67	0
68	0
69	1
70	4
71	26
72	45
73	120
74	28
75	1
76	0
77	0
78	0
79	0
80	1
81	1
82	5
83	15
84	57
85	126
86	247
87	36
88	1
89	0
90	0

n	a(n)
0	0
1	0
2	1
3	0
4	1
5	0
6	0
7	1
8	0
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	1
18	1
19	0
20	0
21	0
22	0
23	1
24	3
25	1
26	0
27	0
28	0
29	0
30	1
31	4
32	6
33	1
34	0
35	0
36	0
37	0
38	1
39	2
40	11
41	10
42	1
43	0
44	0
45	0
46	0
47	0
48	4
49	6
50	26
51	15
52	1
53	0
54	0
55	0
56	0
57	0
58	1
59	11
60	16
61	57
62	21
63	1
64	0
65	0
66	0
67	0
68	0
69	1
70	4
71	26
72	45
73	120
74	28
75	1
76	0
77	0
78	0
79	0
80	1
81	1
82	5
83	15
84	57
85	126
86	247
87	36
88	1
89	0
90	0

n	a(n)
0	0
1	0
2	1
3	0
4	1
5	0
6	0
7	1
8	0
9	0
10	0
11	0
12	1
13	0
14	0
15	0
16	0
17	1
18	1
19	0
20	0
21	0
22	0
23	1
24	3
25	1
26	0
27	0
28	0
29	0
30	1
31	4
32	6
33	1
34	0
35	0
36	0
37	0
38	1
39	2
40	11
41	10
42	1
43	0
44	0
45	0
46	0
47	0
48	4
49	6
50	26
51	15
52	1
53	0
54	0
55	0
56	0
57	0
58	1
59	11
60	16
61	57
62	21
63	1
64	0
65	0
66	0
67	0
68	0
69	1
70	4
71	26
72	45
73	120
74	28
75	1
76	0
77	0
78	0
79	0
80	1
81	1
82	5
83	15
84	57
85	126
86	247
87	36
88	1
89	0
90	0