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

1,20

Comments

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

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

Example

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;

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).

Sequence in context: A185206 A185205 A029295 * A217522 A287520 A130094

Adjacent sequences: A185201 A185202 A185203 * A185205 A185206 A185207

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Feb 22 2011

Extensions

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

Status

approved