A185140 Irregular triangle E(n,g) counting not necessarily connected 4-regular simple graphs on n vertices with girth exactly g.

1, 1, 2, 5, 1, 16, 0, 58, 2, 264, 2, 1535, 12, 10755, 31, 87973, 220, 803973, 1606, 8020967, 16829, 86029760, 193900, 983431053, 2452820, 11913921910, 32670331, 1, 152352965278, 456028487, 2, 2050065073002, 6636066126, 8, 28466234288520, 100135577863, 131, 8020967, 16829

Offset: 5

Author

Jason Kimberley, Jan 06 2013

Keywords

• nonn
• hard
• tabf

Comments

The first column is for girth at least 3. The column for girth g commences when n reaches A037233(g).

Examples

			05: 1;
06: 1;
07: 2;
08: 5, 1;
09: 16, 0;
10: 58, 2;
11: 264, 2;
12: 1535, 12;
13: 10755, 31;
14: 87973, 220;
15: 803973, 1606;
16: 8020967, 16829;
17: 86029760, 193900;
18: 983431053, 2452820;
19: 11913921910, 32670331, 1;
20: 152352965278, 456028487, 2;
21: 2050065073002, 6636066126, 8;
22: 28466234288520, 100135577863, 131;
		

Links

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

Crossrefs

Initial columns of this triangle: A185143 (g=3), A185144 (g=4).

Formula

The n-th row is the sequence of differences of the n-th row of A185340:

E(n,g) = A185340(n,g) - A185340(n,g+1), once we have appended 0 to each row of A185340.

Hence the sum of the n-th row is A185340(n,3) = A033301(n).