login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341853 Number of triangulations of a fixed pentagon with n internal nodes. 3
5, 21, 105, 595, 3675, 24150, 166257, 1186680, 8717940, 65572325, 502957455, 3922142574, 31021294850, 248377859100, 2010068042625, 16421073515280, 135277629836412, 1122788441510820, 9381874768828100, 78871575753345375, 666727830129370275 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

These may be called rooted [n,2] triangulations.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

FORMULA

a(n) = 210*binomial(4*n+5, n)/((3*n+6)*(3*n+7)).

EXAMPLE

The a(0) = 5 triangulations correspond with the dissections of a pentagon by nonintersecting diagonals into 3 triangles. Although there is only one essentially different dissection, each rotation is counted separately here.

MATHEMATICA

Array[210 Binomial[4 # + 5, #]/((3 # + 6)*(3 # + 7)) &, 21, 0] (* Michael De Vlieger, Feb 22 2021 *)

PROG

(PARI) a(n) = {210*binomial(4*n+5, n)/((3*n+6)*(3*n+7))}

CROSSREFS

Column k=2 of A146305.

Sequence in context: A097175 A100284 A337168 * A260845 A325157 A218299

Adjacent sequences:  A341850 A341851 A341852 * A341854 A341855 A341856

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Feb 21 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 19 03:10 EDT 2022. Contains 356216 sequences. (Running on oeis4.)