A185206 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 6.

0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 3, 1, 0, 3, 1, 1, 5, 1, 0, 5, 1, 1, 7, 1, 0, 8, 1, 1, 10, 1, 0, 11, 1, 1, 15, 1, 0, 16, 1, 1, 20, 1, 0, 23, 1, 1, 28, 1, 1, 0, 31, 0, 1, 1, 39, 1, 1, 0, 43, 0, 1, 1, 52, 6, 1, 0, 59, 0, 1, 1, 70, 37, 1, 0, 79, 0

Offset

1,28

Links

Table of n, a(n) for n=1..99.

Jason Kimberley, Disconnected regular graphs with girth at least 6

Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g

Example

1: 0;
2: 1;
3: 1;
4: 1, 1;
5: 1, 0;
6: 1, 1;
7: 1, 0;
8: 1, 1;
9: 1, 0;
10: 1, 1;
11: 1, 0;
12: 1, 1, 1;
13: 1, 0, 1;
14: 1, 1, 2;
15: 1, 0, 2;
16: 1, 1, 3;
17: 1, 0, 3;
18: 1, 1, 5;
19: 1, 0, 5;
20: 1, 1, 7;
21: 1, 0, 8;
22: 1, 1, 10;
23: 1, 0, 11;
24: 1, 1, 15;
25: 1, 0, 16;
26: 1, 1, 20;
27: 1, 0, 23;
28: 1, 1, 28, 1;
29: 1, 0, 31, 0;
30: 1, 1, 39, 1;
31: 1, 0, 43, 0;
32: 1, 1, 52, 6;
33: 1, 0, 59, 0;
34: 1, 1, 70, 37;
35: 1, 0, 79, 0;
36: 1, 1, 95, 432;
37: 1, 0, 106, 0;
38: 1, 1, 125, 8119;
39: 1, 0, 142, 0;
40: 1, 1, 166, 191254;
41: 1, 0, 187, 0;
42: 1, 1, 220, 4855919;
43: 1, 0, 247, 0;
44: 1, 1, 287, 127937854;
45: 1, 0, 325, 0;
46: 1, 1, 375, 3482858263;
47: 1, 0, 423, 0;
48: 1, 1, 490, 98176518259;
49: 1, 0, 551, 0;

Crossrefs

Disconnected k-regular simple graphs with girth at least 6: A185216 (all k), this sequence (triangle); A185226 (k=2), A185236 (k=3), A185246 (k=4).

Sequence in context: A035210 A366750 A185207 * A185205 A029295 A185204

Adjacent sequences: A185203 A185204 A185205 * A185207 A185208 A185209

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Nov 03 2012

Status

approved