A005495 -id:A005495 - cp's OEIS frontend

A005502 Number of unrooted triangulations of a hexagon with n internal nodes.

3, 11, 53, 295, 1867, 12560, 89038, 652198, 4903955, 37627699, 293607612, 2323604832, 18614121391, 150704813812, 1231596828200, 10148762396401, 84252059397251, 704122279126074, 5920239345451780, 50051285956517452, 425273487358680290, 3630084126997807369

Offset: 0

N. J. A. Sloane

nonn

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

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P6 -c2m2 [n]". - Manfred Scheucher, Mar 08 2018

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).

Andrew Howroyd, Table of n, a(n) for n = 0..200
G. Brinkmann and B. McKay, Plantri (program for generation of certain types of planar graph)
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

Column k=3 of the array in A169808.

Cf. A005507, A005495.

a(n) = (A005507(n) + A005495(n))/2 (based on Max Alekseyev's formula, cf. A005501 and A005500).

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

Name clarified and terms a(11) and beyond from Andrew Howroyd, Feb 22 2021

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

Original entry on oeis.org

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

N. J. A. Sloane

nonn

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

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).

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

Column k=3 of the array in A169809.

Cf. A005495, A005502.

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

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

cp's OEIS Frontend

A005502 Number of unrooted triangulations of a hexagon with n internal nodes.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Formula

Extensions