A047140 - cp's OEIS frontend

A047140 Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no up-step crosses the line y=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	3
9	1
10	1
11	2
12	4
13	4
14	1
15	1
16	3
17	2
18	8
19	5
20	1
21	1
22	4
23	5
24	10
25	13
26	6
27	1
28	1
29	5
30	9
31	15
32	23
33	19
34	7
35	1
36	1
37	6
38	14
39	24
40	38
41	42
42	26
43	8
44	1
45	1
46	7
47	20
48	38
49	62
50	80
51	68
52	34
53	9
54	1
55	1
56	8
57	27
58	58
59	38
60	142
61	148
62	102
63	43
64	10
65	1
66	1
67	9
68	35
69	85
70	96
71	180
72	290

[1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 4, 4, 1, 1, 3, 2, 8, 5, 1, 1, 4, 5, 10, 13, 6, 1, 1, 5, 9, 15, 23, 19, 7, 1, 1, 6, 14, 24, 38, 42, 26, 8, 1, 1, 7, 20, 38, 62, 80, 68, 34, 9, 1, 1, 8, 27, 58, 38, 142, 148, 102, 43, 10, 1, 1, 9, 35, 85, 96, 180, 290]

cp's OEIS Frontend

A047140 Array read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no up-step crosses the line y=4x/3. (Thus a path crosses the line only at lattice points and on right-steps.).

Table of values

List of values

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	3
9	1
10	1
11	2
12	4
13	4
14	1
15	1
16	3
17	2
18	8
19	5
20	1
21	1
22	4
23	5
24	10
25	13
26	6
27	1
28	1
29	5
30	9
31	15
32	23
33	19
34	7
35	1
36	1
37	6
38	14
39	24
40	38
41	42
42	26
43	8
44	1
45	1
46	7
47	20
48	38
49	62
50	80
51	68
52	34
53	9
54	1
55	1
56	8
57	27
58	58
59	38
60	142
61	148
62	102
63	43
64	10
65	1
66	1
67	9
68	35
69	85
70	96
71	180
72	290

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	3
9	1
10	1
11	2
12	4
13	4
14	1
15	1
16	3
17	2
18	8
19	5
20	1
21	1
22	4
23	5
24	10
25	13
26	6
27	1
28	1
29	5
30	9
31	15
32	23
33	19
34	7
35	1
36	1
37	6
38	14
39	24
40	38
41	42
42	26
43	8
44	1
45	1
46	7
47	20
48	38
49	62
50	80
51	68
52	34
53	9
54	1
55	1
56	8
57	27
58	58
59	38
60	142
61	148
62	102
63	43
64	10
65	1
66	1
67	9
68	35
69	85
70	96
71	180
72	290

n	a(n)
0	1
1	1
2	1
3	1
4	2
5	1
6	1
7	1
8	3
9	1
10	1
11	2
12	4
13	4
14	1
15	1
16	3
17	2
18	8
19	5
20	1
21	1
22	4
23	5
24	10
25	13
26	6
27	1
28	1
29	5
30	9
31	15
32	23
33	19
34	7
35	1
36	1
37	6
38	14
39	24
40	38
41	42
42	26
43	8
44	1
45	1
46	7
47	20
48	38
49	62
50	80
51	68
52	34
53	9
54	1
55	1
56	8
57	27
58	58
59	38
60	142
61	148
62	102
63	43
64	10
65	1
66	1
67	9
68	35
69	85
70	96
71	180
72	290