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

Author

Jason Kimberley, Nov 03 2012

Keywords

• nonn
• hard
• tabf

Examples

			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;
		

Links

• 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

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).