The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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. 5

%I #15 Sep 21 2022 15:16:57

%S 5,21,105,595,3675,24150,166257,1186680,8717940,65572325,502957455,

%T 3922142574,31021294850,248377859100,2010068042625,16421073515280,

%U 135277629836412,1122788441510820,9381874768828100,78871575753345375,666727830129370275

%N Number of triangulations of a fixed pentagon with n internal nodes.

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

%H Andrew Howroyd, <a href="/A341853/b341853.txt">Table of n, a(n) for n = 0..500</a>

%H K. A. Penson, K. Górska, A. Horzela, and G. H. E. Duchamp, <a href="https://arxiv.org/abs/2209.06574">Hausdorff moment problem for combinatorial numbers of Brown and Tutte: exact solution</a>, arXiv:2209.06574 [math.CO], 2022.

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

%e 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.

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

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

%Y Column k=2 of A146305.

%K nonn

%O 0,1

%A _Andrew Howroyd_, Feb 21 2021

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 May 24 07:02 EDT 2024. Contains 372772 sequences. (Running on oeis4.)