A005507 Number of unrooted triangulations with reflection symmetry of a hexagon with n internal nodes.

2, 6, 18, 52, 166, 524, 1722, 5664, 19072, 64408, 220676, 758864, 2634734, 9180872, 32208376, 113371636, 401067522, 1423073892, 5068961452, 18103192360, 64853607912, 232872927444, 838311889890, 3023961593292, 10931277735230, 39586258360246, 143617299291242

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,3]-triangulations.

References

• C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327-355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)
• C. F. Earl & N. J. A. Sloane, Correspondence, 1980-1981

Crossrefs

Column k=3 of the array in A169809.

Cf. A005495, A005502.

Formula

a(n) = 2 * A005502(n) - A005495(n) (based on Max Alekseyev's formula, cf. A005500 and A005501).

Extensions

a(5)-a(10) from Altug Alkan and Manfred Scheucher, Mar 08 2018

Name clarified and terms a(11) and beyond from Andrew Howroyd, Feb 21 2021