A005028 -id:A005028 - cp's OEIS frontend

A169807 Erroneous version of A005028.

Original entry on oeis.org

1, 2, 4, 12, 33, 102, 312, 1006

Offset: 3

dead

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.

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)

A169809 Array T(n,k) read by antidiagonals: T(n,k) is the number of [n,k]-triangulations in the plane that have reflection symmetry, n >= 0, k >= 0.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 3, 4, 3, 2, 6, 7, 10, 8, 5, 8, 18, 19, 29, 23, 5, 18, 26, 52, 57, 86, 68, 14, 23, 68, 82, 166, 176, 266, 215, 14, 56, 91, 220, 270, 524, 557, 844, 680, 42, 70, 248, 321, 769, 890, 1722, 1806, 2742, 2226, 42, 180, 318, 872, 1151, 2568, 2986, 5664, 5954, 9032, 7327

Offset: 0

N. J. A. Sloane, May 25 2010

"A closed bounded region in the plane divided into triangular regions with k+3 vertices on the boundary and n internal vertices is said to be a triangular map of type [n,k]." It is a [n,k]-triangulation if there are no multiple edges.

"... may be evaluated from the results given by Brown."

			Array begins:
====================================================
n\k |   0   1    2    3     4     5     6      7
----+-----------------------------------------------
  0 |   1   1    1    2     2     5     5     14 ...
  1 |   1   2    3    6     8    18    23     56 ...
  2 |   1   4    7   18    26    68    91    248 ...
  3 |   3  10   19   52    82   220   321    872 ...
  4 |   8  29   57  166   270   769  1151   3296 ...
  5 |  23  86  176  524   890  2568  4020  11558 ...
  6 |  68 266  557 1722  2986  8902 14197  42026 ...
  7 | 215 844 1806 5664 10076 30362 49762 148208 ...
  ...

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.

Andrew Howroyd, Table of n, a(n) for n = 0..1325
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.
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)

Columns k=0..3 are A002712, A005505, A005506, A005507.
Rows n=0..2 are A208355, A005508, A005509.
Antidiagonal sums give A005028.
Cf. A146305 (rooted), A169808 (unrooted), A262586 (oriented).

\\ See link in A169808 for script.
A169809Array(7) \\ Andrew Howroyd, Feb 22 2021

Edited and terms a(36) and beyond from Andrew Howroyd, Feb 22 2021

A005027 Number of trivalent maps with n nodes.

Original entry on oeis.org

1, 2, 4, 16, 63, 328, 1933, 12633, 87466, 633015, 4717745, 35980100, 279418926, 2202903618, 17590599410, 142025760202, 1157868883224, 9520828261067, 78888071847324, 658158709983945, 5525145717439001, 46644670326913204, 395812792437224022, 3374572617006946447

Offset: 3

N. J. A. Sloane

nonn

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 = 3..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)

Antidiagonal sums of array in A169808.

\\ See link in A169808 for script.
A169808AntidiagonalSums(25) \\ Andrew Howroyd, Feb 22 2021

a(n) = (A005028(n) + A341855(n))/2. - Andrew Howroyd, Feb 22 2021

a(10) corrected and terms a(11) and beyond from Andrew Howroyd, Feb 22 2021

A341855 Number of nonseparable trivalent maps with n nodes up to orientation preserving automorphisms.

Original entry on oeis.org

1, 2, 4, 20, 93, 554, 3554, 24256, 171676, 1255194, 9399396, 71837656, 558420702, 4404369524, 35176227916, 284034186632, 2315677128324, 19041443086870, 157775390173844, 1316314747361426, 11050281929647605, 93289306725561418, 791625463473512860, 6749144798353446552

Offset: 3

Andrew Howroyd, Feb 22 2021

nonn

Antidiagonal sums of A262586.

Cf. A005027, A005028.

cp's OEIS Frontend

A169807 Erroneous version of A005028.

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A169809 Array T(n,k) read by antidiagonals: T(n,k) is the number of [n,k]-triangulations in the plane that have reflection symmetry, n >= 0, k >= 0.

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A005027 Number of trivalent maps with n nodes.

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A341855 Number of nonseparable trivalent maps with n nodes up to orientation preserving automorphisms.

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