A128975 - cp's OEIS frontend

A128975 a(n) = the number of unordered triples of integers (a,b,c) with a+b+c=n, whose bitwise XOR is zero. Equivalently, the number of three-heap nim games with n stones which are in a losing position for the first player.

n	a(n)
1	0
2	0
3	0
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	0
12	1
13	0
14	4
15	0
16	0
17	0
18	1
19	0
20	1
21	0
22	4
23	0
24	1
25	0
26	4
27	0
28	4
29	0
30	13
31	0
32	0
33	0
34	1
35	0
36	1
37	0
38	4
39	0
40	1
41	0
42	4
43	0
44	4
45	0
46	13
47	0
48	1
49	0
50	4
51	0
52	4
53	0
54	13
55	0
56	4
57	0
58	13
59	0
60	13
61	0
62	40
63	0
64	0
65	0
66	1
67	0
68	1
69	0
70	4
71	0
72	1
73	0
74	4
75	0
76	4
77	0
78	13
79	0
80	1
81	0
82	4
83	0
84	4
85	0
86	13
87	0
88	4
89	0
90	13
91	0
92	13
93	0
94	40
95	0
96	1
97	0
98	4
99	0
100	4
101	0

[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 1, 0, 4, 0, 4, 0, 13, 0, 4, 0, 13, 0, 13, 0, 40, 0, 0, 0, 1, 0, 1, 0, 4, 0, 1, 0, 4, 0, 4, 0, 13, 0, 1, 0, 4, 0, 4, 0, 13, 0, 4, 0, 13, 0, 13, 0, 40, 0, 1, 0, 4, 0, 4, 0]

cp's OEIS Frontend

A128975 a(n) = the number of unordered triples of integers (a,b,c) with a+b+c=n, whose bitwise XOR is zero. Equivalently, the number of three-heap nim games with n stones which are in a losing position for the first player.

Table of values

List of values

n	a(n)
1	0
2	0
3	0
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	0
12	1
13	0
14	4
15	0
16	0
17	0
18	1
19	0
20	1
21	0
22	4
23	0
24	1
25	0
26	4
27	0
28	4
29	0
30	13
31	0
32	0
33	0
34	1
35	0
36	1
37	0
38	4
39	0
40	1
41	0
42	4
43	0
44	4
45	0
46	13
47	0
48	1
49	0
50	4
51	0
52	4
53	0
54	13
55	0
56	4
57	0
58	13
59	0
60	13
61	0
62	40
63	0
64	0
65	0
66	1
67	0
68	1
69	0
70	4
71	0
72	1
73	0
74	4
75	0
76	4
77	0
78	13
79	0
80	1
81	0
82	4
83	0
84	4
85	0
86	13
87	0
88	4
89	0
90	13
91	0
92	13
93	0
94	40
95	0
96	1
97	0
98	4
99	0
100	4
101	0

n	a(n)
1	0
2	0
3	0
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	0
12	1
13	0
14	4
15	0
16	0
17	0
18	1
19	0
20	1
21	0
22	4
23	0
24	1
25	0
26	4
27	0
28	4
29	0
30	13
31	0
32	0
33	0
34	1
35	0
36	1
37	0
38	4
39	0
40	1
41	0
42	4
43	0
44	4
45	0
46	13
47	0
48	1
49	0
50	4
51	0
52	4
53	0
54	13
55	0
56	4
57	0
58	13
59	0
60	13
61	0
62	40
63	0
64	0
65	0
66	1
67	0
68	1
69	0
70	4
71	0
72	1
73	0
74	4
75	0
76	4
77	0
78	13
79	0
80	1
81	0
82	4
83	0
84	4
85	0
86	13
87	0
88	4
89	0
90	13
91	0
92	13
93	0
94	40
95	0
96	1
97	0
98	4
99	0
100	4
101	0

n	a(n)
1	0
2	0
3	0
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	0
12	1
13	0
14	4
15	0
16	0
17	0
18	1
19	0
20	1
21	0
22	4
23	0
24	1
25	0
26	4
27	0
28	4
29	0
30	13
31	0
32	0
33	0
34	1
35	0
36	1
37	0
38	4
39	0
40	1
41	0
42	4
43	0
44	4
45	0
46	13
47	0
48	1
49	0
50	4
51	0
52	4
53	0
54	13
55	0
56	4
57	0
58	13
59	0
60	13
61	0
62	40
63	0
64	0
65	0
66	1
67	0
68	1
69	0
70	4
71	0
72	1
73	0
74	4
75	0
76	4
77	0
78	13
79	0
80	1
81	0
82	4
83	0
84	4
85	0
86	13
87	0
88	4
89	0
90	13
91	0
92	13
93	0
94	40
95	0
96	1
97	0
98	4
99	0
100	4
101	0