|
|
A002058
|
|
Number of internal triangles in all triangulations of an (n+1)-gon.
(Formerly M2069 N0817)
|
|
6
|
|
|
2, 14, 72, 330, 1430, 6006, 24752, 100776, 406980, 1634380, 6537520, 26075790, 103791870, 412506150, 1637618400, 6495886320, 25751549340, 102042235620, 404225281200, 1600944863700, 6339741660252, 25103519174844, 99399793096352
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
5,1
|
|
COMMENTS
|
The previous name "Number of partitions of a n-gon into (n-3) parts" was erroneous.
Cayley does not seem to have a combinatorial interpretation of this sequence. He just uses it as an auxiliary sequence, nor am I aware of a combinatorial interpretation in the literature.
(End)
First subdiagonal of the table of V(r,k) on page 240. The values V(11,8) = 24052, V(13,10)= 396800 and V(15,12)= 6547520 of the publication are replaced/corrected in the sequence.
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
G.f. 64*x^5/((1+sqrt(1-4*x))^5*sqrt(1-4*x)). - R. J. Mathar, Nov 27 2011
|
|
PROG
|
(PARI) x='x+O('x^66); Vec(64*x^5/((1+sqrt(1-4*x))^5*sqrt(1-4*x))) \\ Joerg Arndt, Jan 30 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|