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

5,3

Comments

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

Links

Table of n, a(n) for n=5..43.

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 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).

Example

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;

Crossrefs

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

Sequence in context: A216962 A186756 A184940 * A111797 A122104 A216121

Adjacent sequences: A185137 A185138 A185139 * A185141 A185142 A185143

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Jan 06 2013

Status

approved