

A169809


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


8



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
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OFFSET

0,5


COMMENTS

"A closed bounded region in the plane divided into triangular regions with n+3 vertices on the boundary and k internal vertices is said to be a triangular map of type [k,n]." It is a [k,n]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. 327355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979.


LINKS

Table of n, a(n) for n=0..35.
William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s314 (1964) 746768.
C. F. Earl and L. J. March, Architectural applications of graph theory, pp. 327355 of R. J. Wilson and L. W. Beineke, editors, Applications of Graph Theory. Academic Press, NY, 1979. (Annotated scanned copy)


EXAMPLE

Array begins:
1,1,1,3,8,23,68,215,680,2226,7327,24607,83060,284046,975950,3383343, ...
1,2,4,10,29,86,266, ...
1,3,7,19,57,176, ...
2,6,18,52,166, ...
2,8,26,82, ...
...


CROSSREFS

Rows are A002712, A005505, A005506, A005507.
Columns are (presumably) A000108 repeated, A005508, A005509.
Antidiagonal sums give A005028.
Cf. A169808.
Sequence in context: A175792 A196686 A213088 * A214962 A076258 A259576
Adjacent sequences: A169806 A169807 A169808 * A169810 A169811 A169812


KEYWORD

nonn,tabl,more


AUTHOR

N. J. A. Sloane, May 25 2010


STATUS

approved



