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A316629 a(n) is the Sprague-Grundy value of the Node-Kayles game on the semi-regular graph of n linked 4-cycles with vertex set {u_1, u_2, ..., u_n, u_{n+1}, v_1, w_1, v_2, w_2, ..., v_n, w_n}. In this graph, u_1, u_2, ..., u_n, and u_{n+1} form a path, and additional edges are given by {u_i, v_i}, {v_i, w_i}, and {w_i, u_{i+1}} for all i=1,2,...,n.

Table of values

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

List of values

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