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.

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

Author

N. J. A. Sloane, Dec 13 2004

Keywords

• nonn
• tabl

Comments

The entries in the first two rows are "by convention".

Examples

			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, ...
		

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.

Crossrefs

Row sums give A005966. First column is A005964 (trivalent connected planar graphs with 2n nodes). Second and third columns give A101205, A101206.