

A169808


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


9



1, 1, 1, 1, 2, 1, 3, 4, 5, 4, 4, 11, 14, 18, 16, 12, 28, 53, 69, 88, 78, 27, 91, 178, 295, 396, 489, 457, 82, 311, 685, 1196, 1867, 2503, 3071, 2938
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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.
T(n,k) is the number of floor plan arrangements represented by 3connected trivalent maps with k internal rooms and n+3 rooms adjacent to the outside.
"... 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:
1,1,1,4,16,78,457,2938,20118,144113,1065328,8068332,62297808,488755938, ...
1,2,5,18,88,489,3071, ...
1,4,14,69,396,2503, ...
3,11,53,295,1867, ...
4,28,178,1196, ...
...


CROSSREFS

Rows are A002713, A005500, A005501, A005502.
Columns are A000207, A005503, A005504.
Antidiagonal sums give A005027.
Cf. A169809.
Sequence in context: A279436 A082470 A101204 * A283069 A304528 A175499
Adjacent sequences: A169805 A169806 A169807 * A169809 A169810 A169811


KEYWORD

nonn,tabl,more


AUTHOR

N. J. A. Sloane, May 25 2010


STATUS

approved



