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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 (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 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 3-connected 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. 327-355 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. 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:

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 A175499 A181440

Adjacent sequences:  A169805 A169806 A169807 * A169809 A169810 A169811

KEYWORD

nonn,tabl,more

AUTHOR

N. J. A. Sloane, May 25 2010

STATUS

approved

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Last modified November 21 17:20 EST 2017. Contains 295004 sequences.