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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
0, 7, 640, 170555, 94949400, 95830621425, 159062872168200, 404720953797785625 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 21:09 EST 2016. Contains 278755 sequences.