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

Author

Jason Kimberley, Dec 26 2012

Keywords

• nonn
• hard
• tabf

Comments

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

Examples

			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;
		

Links

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

Crossrefs

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

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).