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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 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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