A185305 Triangular array E(n,k) counting not necessarily connected k-regular simple graphs on n vertices with girth at least 5.

1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 0, 1, 1, 3, 2, 1, 0, 3, 0, 1, 1, 4, 9, 1, 0, 5, 0, 1, 1, 6, 49, 1, 0, 7, 0, 1, 1, 9, 455, 1, 0, 10, 0, 1, 1, 1, 13, 5784, 2, 1, 0, 15, 0, 8, 1, 1, 18, 90940, 131, 1, 0, 21, 0, 3917, 1, 1, 26, 1620491, 123859

Offset: 1

Author

Jason Kimberley, Feb 21 2013

Keywords

• nonn
• hard
• tabf

Comments

Row sums give A185315.

Examples

			01: 1;
02: 1, 1;
03: 1, 0;
04: 1, 1;
05: 1, 0, 1;
06: 1, 1, 1;
07: 1, 0, 1;
08: 1, 1, 1;
09: 1, 0, 1;
10: 1, 1, 2, 1;
11: 1, 0, 2, 0;
12: 1, 1, 3, 2;
13: 1, 0, 3, 0;
14: 1, 1, 4, 9;
15: 1, 0, 5, 0;
16: 1, 1, 6, 49;
17: 1, 0, 7, 0;
18: 1, 1, 9, 455;
19: 1, 0, 10, 0, 1;
20: 1, 1, 13, 5784, 2;
21: 1, 0, 15, 0, 8;
22: 1, 1, 18, 90940, 131;
23: 1, 0, 21, 0, 3917;
24: 1, 1, 26, 1620491, 123859;
25: 1, 0, 30, 0, 4131991;
26: 1, 1, 36, 31478649, 132160608;
27: 1, 0, 42, 0, 4018022149;
28: 1, 1, 50, 656784488, 118369811960;
		

Links

• Jason Kimberley, Table of n, a(i)=E(n,k) for i = 1..108 (n = 1..28)
• Jason Kimberley, Not necessarily connected k-regular graphs with girth at least 5
• Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

Crossrefs

Not necessarily connected k-regular simple graphs with girth at least 5: A185315 (any k), this sequence (triangle); specified degree k: A185325 (k=2), A185335 (k=3).

Formula

E(n,k) = A186715(n,k) + A185205(n,k).