A005505 Number of unrooted triangulations with reflection symmetry of a quadrilateral with n internal nodes. (Formerly M1227)

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

0,2

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

Formula

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

Crossrefs

Column k=1 of the array in A169809.

Cf. A002710, A005500.

Sequence in context: A224845 A148113 A243814 * A262592 A187255 A148114

Adjacent sequences: A005502 A005503 A005504 * A005506 A005507 A005508

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved