A185204 Triangular array D(n,k) counting disconnected k-regular simple graphs on n vertices with girth at least 4.

0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 4, 1, 1, 0, 4, 0, 1, 1, 6, 2, 1, 0, 7, 0, 1, 1, 10, 9, 1, 1, 0, 11, 0, 0, 1, 1, 15, 35, 2, 1, 0, 17, 0, 2, 1, 1, 23, 177, 15, 1, 1, 0, 26, 0, 35, 0, 1, 1, 33, 1153, 247, 1, 1, 0, 38, 0, 1692, 0, 1, 1, 49, 10341, 17409, 8, 1

Offset: 1

Author

Jason Kimberley, Feb 22 2011

Keywords

• nonn
• hard
• tabf

Comments

For n >= 0 and 0 <= k <= A002265(n).

Examples

			0;
1;
1;
1, 1;
1, 0;
1, 1;
1, 0;
1, 1, 1;
1, 0, 1;
1, 1, 2;
1, 0, 2;
1, 1, 4, 1;
1, 0, 4, 0;
1, 1, 6, 2;
1, 0, 7, 0;
1, 1, 10, 9, 1;
1, 0, 11, 0, 0;
1, 1, 15, 35, 2;
1, 0, 17, 0, 2;
		

Links

• Jason Kimberley, Table of i, a(i)=D(n,k) for i = 1..147 (n = 1..32)
• Jason Kimberley, Incomplete table of i, n, k, D(n,k)=a(i) for n = 1..38 (i = 1..209)
• Jason Kimberley, Disconnected k-regular graphs with girth at least 4
• 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 4: A185214 (any k), this sequence (triangle); specified degree k: A185224 (k=2), A185234 (k=3), A185244 (k=4), A185254 (k=5), A185264 (k=6), A185274 (k=7), A185284 (k=8), A185294 (k=9).

Extensions

The b-file corrected and a-file expanded by the author, Jan 19 2013