A169808 -id:A169808 - 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

A005504 Number of unrooted triangulations of a disk with 2 internal nodes and n+3 nodes on the boundary.

Original entry on oeis.org

1, 5, 14, 53, 178, 685, 2548, 9876, 37950, 147520, 572594, 2230735, 8693932, 33939465, 132598484, 518607032, 2029990774, 7952788446, 31179668572, 122331725930, 480283816348, 1886829349570, 7416950176904, 29171683995320, 114795961678380, 451968102200966, 1780298693036010

Offset: 0

N. J. A. Sloane

nonn

These are also called [2,n]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P[n] -c2m2 [n+2]". - 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..500
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

Row n=2 of the array in A169808.

a(6)-a(12) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(13) and beyond from Andrew Howroyd, Feb 22 2021

A005503 Number of unrooted triangulations of a disk with one internal node and n+3 nodes on the boundary.

Original entry on oeis.org

1, 2, 4, 11, 28, 91, 291, 1004, 3471, 12350, 44114, 159519, 579835, 2121845, 7800702, 28813730, 106844383, 397647256, 1484755972, 5560561040, 20881939915, 78617991116, 296678132514, 1121988213996, 4251702739831, 16141719280994, 61389611762126, 233856524866209

Offset: 0

N. J. A. Sloane

nonn

These are also called [1,n]-triangulations.

Graphs can be enumerated and counted using the tool "plantri", in particular the command "./plantri -s -P[n] -c2m2 [n+1]". - 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).

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

Row n=1 of the array in A169808.

a(6) corrected and a(7)-a(14) from Manfred Scheucher, Mar 08 2018

Name clarified and terms a(15) and beyond from Andrew Howroyd, Feb 22 2021

A378190 Number of planar maps with an external face and n internal triangular faces.

Original entry on oeis.org

1, 2, 6, 24, 100, 586, 3725, 26532, 198081, 1539550, 12274565, 99959181, 827795678, 6954099320, 59138955508, 508331799502, 4410651891166, 38590663253312, 340173195849485, 3018768835038348, 26952060900042852, 241960993507098580, 2183134755112963493, 19788571100313277286

Offset: 1

Ya-Ping Lu, Nov 19 2024

nonn

Column sums of A378103.

Cf. A002713, A169808, A377785.

a(n) = (A378337(n) + A378341(n))/2.

cp's OEIS Frontend

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

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A005504 Number of unrooted triangulations of a disk with 2 internal nodes and n+3 nodes on the boundary.

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Author

Keywords

Comments

References

Links

Crossrefs

Extensions

A005503 Number of unrooted triangulations of a disk with one internal node and n+3 nodes on the boundary.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions

A378190 Number of planar maps with an external face and n internal triangular faces.

Views

Author

Keywords

Crossrefs

Formula