A185130 Irregular triangle E(n,g) counting not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g.

1, 1, 1, 4, 2, 15, 5, 1, 71, 21, 2, 428, 103, 8, 1, 3406, 752, 48, 1, 34270, 7385, 450, 5, 418621, 91939, 5752, 32, 5937051, 1345933, 90555, 385, 94782437, 22170664, 1612917, 7573, 1, 1670327647, 401399440, 31297424, 181224, 3, 32090011476, 7887389438

Offset

2,4

Comments

The first column is for girth exactly 3. The column for girth exactly g begins when 2n reaches A000066(g).

Links

Table of n, a(n) for n=2..44.

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

Formula

The n-th row is the sequence of differences of the n-th row of A185330:

E(n,g) = A185330(n,g) - A185330(n,g+1), once we have appended 0 to each row of A185330.

Hence the sum of the n-th row is A185330(n,3) = A005638(n).

Example

1;
1, 1;
4, 2;
15, 5, 1;
71, 21, 2;
428, 103, 8, 1;
3406, 752, 48, 1;
34270, 7385, 450, 5;
418621, 91939, 5752, 32;
5937051, 1345933, 90555, 385;
94782437, 22170664, 1612917, 7573, 1;
1670327647, 401399440, 31297424, 181224, 3;
32090011476, 7887389438, 652159986, 4624481, 21;
666351752261, 166897766824, 14499787794, 122089999, 545, 1;
14859579573845, 3781593764772, 342646826428, 3328899592, 30368, 0;

Crossrefs

Initial columns of this triangle: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Sequence in context: A019061 A019012 A154333 * A261870 A325516 A299789

Adjacent sequences: A185127 A185128 A185129 * A185131 A185132 A185133

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Dec 26 2012

Status

approved