A134423 - cp's OEIS frontend

A134423 Triangle read by rows: T(n,k) is the number of paths in the first quadrant from (0,0) to (n,0) using steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), such that the area between the x-axis and the path is k (n>=0, 0<=k<=floor(n^2/4)).

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	2
6	1
7	5
8	5
9	3
10	2
11	1
12	8
13	10
14	8
15	6
16	5
17	2
18	1
19	13
20	20
21	19
22	17
23	16
24	11
25	7
26	3
27	2
28	1
29	21
30	38
31	42
32	42
33	43
34	36
35	29
36	18
37	12
38	8
39	5
40	2
41	1
42	34
43	71
44	89
45	98
46	108
47	102
48	92
49	72
50	55
51	40
52	29
53	20
54	13
55	7
56	3
57	2
58	1
59	55
60	130
61	182
62	218
63	255
64	264
65	258
66	228
67	195
68	158
69	125
70	96
71	74
72	52
73	35
74	22
75	14
76	8

[1, 1, 2, 1, 3, 2, 1, 5, 5, 3, 2, 1, 8, 10, 8, 6, 5, 2, 1, 13, 20, 19, 17, 16, 11, 7, 3, 2, 1, 21, 38, 42, 42, 43, 36, 29, 18, 12, 8, 5, 2, 1, 34, 71, 89, 98, 108, 102, 92, 72, 55, 40, 29, 20, 13, 7, 3, 2, 1, 55, 130, 182, 218, 255, 264, 258, 228, 195, 158, 125, 96, 74, 52, 35, 22, 14, 8]

cp's OEIS Frontend

A134423 Triangle read by rows: T(n,k) is the number of paths in the first quadrant from (0,0) to (n,0) using steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), such that the area between the x-axis and the path is k (n>=0, 0<=k<=floor(n^2/4)).

Table of values

List of values

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	2
6	1
7	5
8	5
9	3
10	2
11	1
12	8
13	10
14	8
15	6
16	5
17	2
18	1
19	13
20	20
21	19
22	17
23	16
24	11
25	7
26	3
27	2
28	1
29	21
30	38
31	42
32	42
33	43
34	36
35	29
36	18
37	12
38	8
39	5
40	2
41	1
42	34
43	71
44	89
45	98
46	108
47	102
48	92
49	72
50	55
51	40
52	29
53	20
54	13
55	7
56	3
57	2
58	1
59	55
60	130
61	182
62	218
63	255
64	264
65	258
66	228
67	195
68	158
69	125
70	96
71	74
72	52
73	35
74	22
75	14
76	8

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	2
6	1
7	5
8	5
9	3
10	2
11	1
12	8
13	10
14	8
15	6
16	5
17	2
18	1
19	13
20	20
21	19
22	17
23	16
24	11
25	7
26	3
27	2
28	1
29	21
30	38
31	42
32	42
33	43
34	36
35	29
36	18
37	12
38	8
39	5
40	2
41	1
42	34
43	71
44	89
45	98
46	108
47	102
48	92
49	72
50	55
51	40
52	29
53	20
54	13
55	7
56	3
57	2
58	1
59	55
60	130
61	182
62	218
63	255
64	264
65	258
66	228
67	195
68	158
69	125
70	96
71	74
72	52
73	35
74	22
75	14
76	8

n	a(n)
0	1
1	1
2	2
3	1
4	3
5	2
6	1
7	5
8	5
9	3
10	2
11	1
12	8
13	10
14	8
15	6
16	5
17	2
18	1
19	13
20	20
21	19
22	17
23	16
24	11
25	7
26	3
27	2
28	1
29	21
30	38
31	42
32	42
33	43
34	36
35	29
36	18
37	12
38	8
39	5
40	2
41	1
42	34
43	71
44	89
45	98
46	108
47	102
48	92
49	72
50	55
51	40
52	29
53	20
54	13
55	7
56	3
57	2
58	1
59	55
60	130
61	182
62	218
63	255
64	264
65	258
66	228
67	195
68	158
69	125
70	96
71	74
72	52
73	35
74	22
75	14
76	8