A342053 - OEIS

A342053

Array read by antidiagonals: T(n,k) is the number of unrooted 3-connected triangulations of a disk with n interior nodes and k nodes on the boundary, n >= 1, k >= 3.

1, 1, 1, 1, 2, 4, 1, 2, 8, 16, 1, 3, 12, 38, 78, 1, 3, 20, 73, 219, 457, 1, 4, 27, 140, 503, 1404, 2938, 1, 4, 39, 235, 1089, 3661, 9714, 20118, 1, 5, 51, 392, 2149, 8796, 27715, 70454, 144113, 1, 5, 68, 610, 4050, 19419, 72204, 214664, 527235, 1065328

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OFFSET

1,5

COMMENTS

For k >= 4, T(n,k) is the number of polyhedra with n+k vertices whose faces are all triangular, except one which is k-gonal.

The initial terms of this sequence can also be computed using the tool "plantri", in particular the command "./plantri -u -v -P [n]" will compute values for a diagonal.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

G. Brinkmann and B. McKay, Plantri (program for generation of certain types of planar graph)

William G. Brown, Enumeration of Triangulations of the Disk, Proc. Lond. Math. Soc. s3-14 (1964) 746-768.

Andrew Howroyd, PARI Program

EXAMPLE

Array begins:

===================================================

n\k | 3 4 5 6 7 8

----+----------------------------------------------

1 | 1 1 1 1 1 1 ...

2 | 1 2 2 3 3 4 ...