A005505 Number of unrooted triangulations with reflection symmetry of a quadrilateral with n internal nodes.

1, 2, 4, 10, 29, 86, 266, 844, 2742, 9032, 30202, 101988, 347914, 1195500, 4138310, 14405848, 50428392, 177321636, 626250990, 2219876580, 7896651847, 28176271634, 100830069380, 361757157484, 1301092926454, 4689840961196, 16940093338162, 61305930699382

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are also called [n,1]-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..500
• 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=1 of the array in A169809.

Cf. A002710, A005500.

Formula

a(n) = 2 * A005500(n) - A002710(n) (based on Max Alekseyev's formula, cf. A005500).

Extensions

a(7)-a(12) from Altug Alkan and Manfred Scheucher, Mar 08 2018

Name clarified and terms a(13) and beyond from Andrew Howroyd, Feb 21 2021