A097098 - cp's OEIS frontend

A097098 Triangle read by rows: T(n,k) is the number of peakless Motzkin paths of length n and having a total of k level steps (1,0) to the left of the first (1,1) step and to the right of the last (1,-1) step (i.e., total length of the two tails is k; can be easily expressed in terms of RNA secondary structure terminology).

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	0
13	0
14	1
15	2
16	2
17	3
18	0
19	0
20	1
21	5
22	4
23	3
24	4
25	0
26	0
27	1
28	11
29	10
30	6
31	4
32	5
33	0
34	0
35	1
36	25
37	22
38	15
39	8
40	5
41	6
42	0
43	0
44	1
45	58
46	50
47	33
48	20
49	10
50	6
51	7
52	0
53	0
54	1
55	135
56	116
57	75
58	44
59	25
60	12
61	7
62	8
63	0
64	0
65	1
66	317
67	270
68	174
69	100
70	55
71	30
72	14
73	8
74	9
75	0
76	0
77	1
78	750
79	634
80	405
81	232
82	125
83	66
84	35
85	16
86	9
87	10
88	0
89	0
90	1

[1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 2, 2, 3, 0, 0, 1, 5, 4, 3, 4, 0, 0, 1, 11, 10, 6, 4, 5, 0, 0, 1, 25, 22, 15, 8, 5, 6, 0, 0, 1, 58, 50, 33, 20, 10, 6, 7, 0, 0, 1, 135, 116, 75, 44, 25, 12, 7, 8, 0, 0, 1, 317, 270, 174, 100, 55, 30, 14, 8, 9, 0, 0, 1, 750, 634, 405, 232, 125, 66, 35, 16, 9, 10, 0, 0, 1]

cp's OEIS Frontend

Table of values

List of values

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	0
13	0
14	1
15	2
16	2
17	3
18	0
19	0
20	1
21	5
22	4
23	3
24	4
25	0
26	0
27	1
28	11
29	10
30	6
31	4
32	5
33	0
34	0
35	1
36	25
37	22
38	15
39	8
40	5
41	6
42	0
43	0
44	1
45	58
46	50
47	33
48	20
49	10
50	6
51	7
52	0
53	0
54	1
55	135
56	116
57	75
58	44
59	25
60	12
61	7
62	8
63	0
64	0
65	1
66	317
67	270
68	174
69	100
70	55
71	30
72	14
73	8
74	9
75	0
76	0
77	1
78	750
79	634
80	405
81	232
82	125
83	66
84	35
85	16
86	9
87	10
88	0
89	0
90	1

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	0
13	0
14	1
15	2
16	2
17	3
18	0
19	0
20	1
21	5
22	4
23	3
24	4
25	0
26	0
27	1
28	11
29	10
30	6
31	4
32	5
33	0
34	0
35	1
36	25
37	22
38	15
39	8
40	5
41	6
42	0
43	0
44	1
45	58
46	50
47	33
48	20
49	10
50	6
51	7
52	0
53	0
54	1
55	135
56	116
57	75
58	44
59	25
60	12
61	7
62	8
63	0
64	0
65	1
66	317
67	270
68	174
69	100
70	55
71	30
72	14
73	8
74	9
75	0
76	0
77	1
78	750
79	634
80	405
81	232
82	125
83	66
84	35
85	16
86	9
87	10
88	0
89	0
90	1

n	a(n)
0	1
1	0
2	1
3	0
4	0
5	1
6	1
7	0
8	0
9	1
10	1
11	2
12	0
13	0
14	1
15	2
16	2
17	3
18	0
19	0
20	1
21	5
22	4
23	3
24	4
25	0
26	0
27	1
28	11
29	10
30	6
31	4
32	5
33	0
34	0
35	1
36	25
37	22
38	15
39	8
40	5
41	6
42	0
43	0
44	1
45	58
46	50
47	33
48	20
49	10
50	6
51	7
52	0
53	0
54	1
55	135
56	116
57	75
58	44
59	25
60	12
61	7
62	8
63	0
64	0
65	1
66	317
67	270
68	174
69	100
70	55
71	30
72	14
73	8
74	9
75	0
76	0
77	1
78	750
79	634
80	405
81	232
82	125
83	66
84	35
85	16
86	9
87	10
88	0
89	0
90	1