A300953 - cp's OEIS frontend

A300953 Number T(n,k) of Dyck paths of semilength n such that 2*k is the difference between the area above the path and the area below the path, measured within the smallest enclosing rectangle based on the x-axis; triangle T(n,k), n>=0, -floor((n-1)^2/4) <= k <= floor((n-1)^2/4), read by rows.

n	a(n)
0	1
1	1
2	2
3	1
4	2
5	2
6	2
7	0
8	7
9	0
10	5
11	1
12	2
13	3
14	6
15	7
16	8
17	6
18	6
19	3
20	2
21	0
22	9
23	0
24	20
25	0
26	35
27	0
28	34
29	0
30	25
31	0
32	7
33	1
34	2
35	4
36	8
37	10
38	17
39	23
40	30
41	38
42	43
43	46
44	48
45	42
46	41
47	26
48	26
49	12
50	8
51	4
52	2
53	0
54	11
55	0
56	29
57	0
58	63
59	0
60	115
61	0
62	176
63	0
64	238
65	0
66	255
67	0
68	230
69	0
70	169
71	0
72	92
73	0
74	41
75	0
76	9

[1, 1, 2, 1, 2, 2, 2, 0, 7, 0, 5, 1, 2, 3, 6, 7, 8, 6, 6, 3, 2, 0, 9, 0, 20, 0, 35, 0, 34, 0, 25, 0, 7, 1, 2, 4, 8, 10, 17, 23, 30, 38, 43, 46, 48, 42, 41, 26, 26, 12, 8, 4, 2, 0, 11, 0, 29, 0, 63, 0, 115, 0, 176, 0, 238, 0, 255, 0, 230, 0, 169, 0, 92, 0, 41, 0, 9]

cp's OEIS Frontend

A300953 Number T(n,k) of Dyck paths of semilength n such that 2*k is the difference between the area above the path and the area below the path, measured within the smallest enclosing rectangle based on the x-axis; triangle T(n,k), n>=0, -floor((n-1)^2/4) <= k <= floor((n-1)^2/4), read by rows.

Table of values

List of values

n	a(n)
0	1
1	1
2	2
3	1
4	2
5	2
6	2
7	0
8	7
9	0
10	5
11	1
12	2
13	3
14	6
15	7
16	8
17	6
18	6
19	3
20	2
21	0
22	9
23	0
24	20
25	0
26	35
27	0
28	34
29	0
30	25
31	0
32	7
33	1
34	2
35	4
36	8
37	10
38	17
39	23
40	30
41	38
42	43
43	46
44	48
45	42
46	41
47	26
48	26
49	12
50	8
51	4
52	2
53	0
54	11
55	0
56	29
57	0
58	63
59	0
60	115
61	0
62	176
63	0
64	238
65	0
66	255
67	0
68	230
69	0
70	169
71	0
72	92
73	0
74	41
75	0
76	9

n	a(n)
0	1
1	1
2	2
3	1
4	2
5	2
6	2
7	0
8	7
9	0
10	5
11	1
12	2
13	3
14	6
15	7
16	8
17	6
18	6
19	3
20	2
21	0
22	9
23	0
24	20
25	0
26	35
27	0
28	34
29	0
30	25
31	0
32	7
33	1
34	2
35	4
36	8
37	10
38	17
39	23
40	30
41	38
42	43
43	46
44	48
45	42
46	41
47	26
48	26
49	12
50	8
51	4
52	2
53	0
54	11
55	0
56	29
57	0
58	63
59	0
60	115
61	0
62	176
63	0
64	238
65	0
66	255
67	0
68	230
69	0
70	169
71	0
72	92
73	0
74	41
75	0
76	9

n	a(n)
0	1
1	1
2	2
3	1
4	2
5	2
6	2
7	0
8	7
9	0
10	5
11	1
12	2
13	3
14	6
15	7
16	8
17	6
18	6
19	3
20	2
21	0
22	9
23	0
24	20
25	0
26	35
27	0
28	34
29	0
30	25
31	0
32	7
33	1
34	2
35	4
36	8
37	10
38	17
39	23
40	30
41	38
42	43
43	46
44	48
45	42
46	41
47	26
48	26
49	12
50	8
51	4
52	2
53	0
54	11
55	0
56	29
57	0
58	63
59	0
60	115
61	0
62	176
63	0
64	238
65	0
66	255
67	0
68	230
69	0
70	169
71	0
72	92
73	0
74	41
75	0
76	9