A069999 - cp's OEIS frontend

A069999 Number of possible dimensions for commutators of n X n matrices; it is independent of the field. Or, given a partition P = (p_1, p_2, ..., p_m) of n with p_1 >= p_2 >= ... >= p_m, let S(P) = sum_j (2j-1)p_j; then a(n) = number of integers that are an S(P) for some partition.

n	a(n)
0	1
1	1
2	2
3	3
4	5
5	7
6	9
7	13
8	18
9	21
10	27
11	34
12	39
13	46
14	54
15	61
16	72
17	83
18	92
19	106
20	118
21	130
22	145
23	162
24	176
25	193
26	209
27	226
28	246
29	265
30	284
31	308
32	330
33	352
34	375
35	402
36	426
37	453
38	480
39	508
40	538
41	570
42	598
43	631
44	661
45	694
46	730
47	765
48	800
49	835
50	872
51	911
52	951
53	992
54	1030
55	1071
56	1115

[1, 1, 2, 3, 5, 7, 9, 13, 18, 21, 27, 34, 39, 46, 54, 61, 72, 83, 92, 106, 118, 130, 145, 162, 176, 193, 209, 226, 246, 265, 284, 308, 330, 352, 375, 402, 426, 453, 480, 508, 538, 570, 598, 631, 661, 694, 730, 765, 800, 835, 872, 911, 951, 992, 1030, 1071, 1115]

cp's OEIS Frontend

A069999 Number of possible dimensions for commutators of n X n matrices; it is independent of the field. Or, given a partition P = (p_1, p_2, ..., p_m) of n with p_1 >= p_2 >= ... >= p_m, let S(P) = sum_j (2j-1)p_j; then a(n) = number of integers that are an S(P) for some partition.

Table of values

List of values