A109542 a(n) = number of labeled 3-regular (trivalent) multi-graphs without self-loops on 2n vertices with a maximum of 2 edges between any pair of nodes. Also a(n) = number of labeled symmetric 2n X 2n matrices with {0,1,2}-entries with row sum equal to 3 for each row and trace 0.

0, 7, 640, 170555, 94949400, 95830621425, 159062872168200, 404720953797785625

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Example

a(2)=7 because for 2*n=4 nodes there are 7 possible labeled graphs whose adjacency matrices are as follows:
0 2 1 0
2 0 0 1
1 0 0 2
0 1 2 0;
0 1 2 0
1 0 0 2
2 0 0 1
0 2 1 0;
0 2 0 1
2 0 1 0
0 1 0 2
1 0 2 0;
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0;
0 0 2 1
0 0 1 2
2 1 0 0
1 2 0 0;
0 1 0 2
1 0 2 0
0 2 0 1
2 0 1 0;
0 0 1 2
0 0 2 1
1 2 0 0
2 1 0 0.

Crossrefs

Cf. A001205, A002829, A108243.

Sequence in context: A175601 A246113 A277839 * A052132 A052134 A101811

Adjacent sequences: A109539 A109540 A109541 * A109543 A109544 A109545

Keyword

nonn,more

Author

Jeremy Gardiner, Aug 29 2005

Extensions

a(5)-a(8) from Max Alekseyev, Aug 30 2005

Status

approved