A169809 - OEIS

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.

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

"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."

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.

LINKS

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)

EXAMPLE

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 ...