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A101204
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.
2
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
OFFSET
0,9
COMMENTS
The entries in the first two rows are "by convention".
REFERENCES
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.
EXAMPLE
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, ...
CROSSREFS
Row sums give A005966. First column is A005964 (trivalent connected planar graphs with 2n nodes). Second and third columns give A101205, A101206.
Sequence in context: A232095 A279436 A082470 * A169808 A328395 A283069
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Dec 13 2004
STATUS
approved