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A109542
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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.
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0
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OFFSET
| 1,2
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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.
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CROSSREFS
| Cf. A001205, A002829, A108243.
Sequence in context: A087772 A047942 A175601 * A052132 A052134 A101811
Adjacent sequences: A109539 A109540 A109541 * A109543 A109544 A109545
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KEYWORD
| nonn,more
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AUTHOR
| Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Aug 29 2005
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EXTENSIONS
| a(5)-a(8) from Max Alekseyev (maxale(AT)gmail.com), Aug 30 2005
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