A012265 - cp's OEIS frontend

A012265 x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.

n	a(n)
0	0
1	1
2	0
3	1
4	2
5	1
6	2
7	3
8	2
9	3
10	2
11	3
12	4
13	3
14	4
15	3
16	4
17	5
18	4
19	5
20	6
21	5
22	6
23	5
24	6
25	7
26	6
27	7
28	8
29	7
30	8
31	7
32	8
33	9
34	8
35	9
36	8
37	9
38	10
39	9
40	10
41	11
42	10
43	11
44	10
45	11
46	12
47	11
48	12
49	11
50	12
51	13
52	12
53	13
54	14
55	13
56	14
57	13
58	14
59	15
60	14
61	15
62	16

[0, 1, 0, 1, 2, 1, 2, 3, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 16]

cp's OEIS Frontend

A012265 x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)! has 2a(n)+1 real roots.

Table of values

List of values

n	a(n)
0	0
1	1
2	0
3	1
4	2
5	1
6	2
7	3
8	2
9	3
10	2
11	3
12	4
13	3
14	4
15	3
16	4
17	5
18	4
19	5
20	6
21	5
22	6
23	5
24	6
25	7
26	6
27	7
28	8
29	7
30	8
31	7
32	8
33	9
34	8
35	9
36	8
37	9
38	10
39	9
40	10
41	11
42	10
43	11
44	10
45	11
46	12
47	11
48	12
49	11
50	12
51	13
52	12
53	13
54	14
55	13
56	14
57	13
58	14
59	15
60	14
61	15
62	16

n	a(n)
0	0
1	1
2	0
3	1
4	2
5	1
6	2
7	3
8	2
9	3
10	2
11	3
12	4
13	3
14	4
15	3
16	4
17	5
18	4
19	5
20	6
21	5
22	6
23	5
24	6
25	7
26	6
27	7
28	8
29	7
30	8
31	7
32	8
33	9
34	8
35	9
36	8
37	9
38	10
39	9
40	10
41	11
42	10
43	11
44	10
45	11
46	12
47	11
48	12
49	11
50	12
51	13
52	12
53	13
54	14
55	13
56	14
57	13
58	14
59	15
60	14
61	15
62	16

n	a(n)
0	0
1	1
2	0
3	1
4	2
5	1
6	2
7	3
8	2
9	3
10	2
11	3
12	4
13	3
14	4
15	3
16	4
17	5
18	4
19	5
20	6
21	5
22	6
23	5
24	6
25	7
26	6
27	7
28	8
29	7
30	8
31	7
32	8
33	9
34	8
35	9
36	8
37	9
38	10
39	9
40	10
41	11
42	10
43	11
44	10
45	11
46	12
47	11
48	12
49	11
50	12
51	13
52	12
53	13
54	14
55	13
56	14
57	13
58	14
59	15
60	14
61	15
62	16