A345123 - cp's OEIS frontend

A345123 Number T(n,k) of ordered subsequences of {1,...,n} containing at least k elements and such that the first differences contain only odd numbers; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

n	a(n)
0	1
1	2
2	1
3	4
4	3
5	1
6	7
7	6
8	3
9	1
10	12
11	11
12	7
13	3
14	1
15	20
16	19
17	14
18	8
19	3
20	1
21	33
22	32
23	26
24	17
25	9
26	3
27	1
28	54
29	53
30	46
31	34
32	20
33	10
34	3
35	1
36	88
37	87
38	79
39	63
40	43
41	23
42	11
43	3
44	1
45	143
46	142
47	133
48	113
49	83
50	53
51	26
52	12
53	3
54	1
55	232
56	231
57	221
58	196
59	156
60	106
61	64
62	29
63	13
64	3
65	1
66	376
67	375
68	364
69	334
70	279
71	209
72	132
73	76
74	32
75	14
76	3
77	1

[1, 2, 1, 4, 3, 1, 7, 6, 3, 1, 12, 11, 7, 3, 1, 20, 19, 14, 8, 3, 1, 33, 32, 26, 17, 9, 3, 1, 54, 53, 46, 34, 20, 10, 3, 1, 88, 87, 79, 63, 43, 23, 11, 3, 1, 143, 142, 133, 113, 83, 53, 26, 12, 3, 1, 232, 231, 221, 196, 156, 106, 64, 29, 13, 3, 1, 376, 375, 364, 334, 279, 209, 132, 76, 32, 14, 3, 1]

cp's OEIS Frontend

A345123 Number T(n,k) of ordered subsequences of {1,...,n} containing at least k elements and such that the first differences contain only odd numbers; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

Table of values

List of values

n	a(n)
0	1
1	2
2	1
3	4
4	3
5	1
6	7
7	6
8	3
9	1
10	12
11	11
12	7
13	3
14	1
15	20
16	19
17	14
18	8
19	3
20	1
21	33
22	32
23	26
24	17
25	9
26	3
27	1
28	54
29	53
30	46
31	34
32	20
33	10
34	3
35	1
36	88
37	87
38	79
39	63
40	43
41	23
42	11
43	3
44	1
45	143
46	142
47	133
48	113
49	83
50	53
51	26
52	12
53	3
54	1
55	232
56	231
57	221
58	196
59	156
60	106
61	64
62	29
63	13
64	3
65	1
66	376
67	375
68	364
69	334
70	279
71	209
72	132
73	76
74	32
75	14
76	3
77	1

n	a(n)
0	1
1	2
2	1
3	4
4	3
5	1
6	7
7	6
8	3
9	1
10	12
11	11
12	7
13	3
14	1
15	20
16	19
17	14
18	8
19	3
20	1
21	33
22	32
23	26
24	17
25	9
26	3
27	1
28	54
29	53
30	46
31	34
32	20
33	10
34	3
35	1
36	88
37	87
38	79
39	63
40	43
41	23
42	11
43	3
44	1
45	143
46	142
47	133
48	113
49	83
50	53
51	26
52	12
53	3
54	1
55	232
56	231
57	221
58	196
59	156
60	106
61	64
62	29
63	13
64	3
65	1
66	376
67	375
68	364
69	334
70	279
71	209
72	132
73	76
74	32
75	14
76	3
77	1

n	a(n)
0	1
1	2
2	1
3	4
4	3
5	1
6	7
7	6
8	3
9	1
10	12
11	11
12	7
13	3
14	1
15	20
16	19
17	14
18	8
19	3
20	1
21	33
22	32
23	26
24	17
25	9
26	3
27	1
28	54
29	53
30	46
31	34
32	20
33	10
34	3
35	1
36	88
37	87
38	79
39	63
40	43
41	23
42	11
43	3
44	1
45	143
46	142
47	133
48	113
49	83
50	53
51	26
52	12
53	3
54	1
55	232
56	231
57	221
58	196
59	156
60	106
61	64
62	29
63	13
64	3
65	1
66	376
67	375
68	364
69	334
70	279
71	209
72	132
73	76
74	32
75	14
76	3
77	1