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A101204
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Triangle read by rows: T(n,k) = number of planar trivalent (or cubic) loopless multigraphs with 2n nodes and exactly k double bonds, for 0 <= k <= n.
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2
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1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 3, 4, 5, 4, 1, 9, 16, 22, 16, 7, 1, 32, 75, 112, 86, 41, 10, 1, 133
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OFFSET
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0,9
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COMMENTS
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The entries in the first two rows are "by convention".
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REFERENCES
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A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 92.
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LINKS
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EXAMPLE
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Triangle begins
1,
0, 1,
1, 0, 1,
1, 1, 2, 1,
3, 4, 5, 4, 1
9, 16, 22, 16, 7, 1
32, 75, 112, 86, 41, 10, 1
133, ...
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CROSSREFS
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Row sums give A005966. First column is A005964 (trivalent connected planar graphs with 2n nodes). Second and third columns give A101205, A101206.
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KEYWORD
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AUTHOR
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STATUS
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approved
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