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Number of rooted gluings of octahedra with n square vertices.
2

%I #23 Oct 06 2019 07:46:19

%S 1,3,36,594,11340,235467,5164236,117704340,2760422652,66179363580,

%T 1614629242512,39958835859306,1000667989897524,25310418084553770,

%U 645671000841035400,16592979103827051240,429173117580596633820,11163550152596460675012,291848008677713303547312

%N Number of rooted gluings of octahedra with n square vertices.

%H Alois P. Heinz, <a href="/A291096/b291096.txt">Table of n, a(n) for n = 0..691</a>

%H Valentin Bonzom, Luca Lionni, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i3p36">Counting Gluings of Octahedra</a>, Electronic Journal of Combinatorics 24(3) (2017), #P3.36.

%F G.f.: A(x) satisfies A(x) = 1 + 3*x*A(x)^4.

%F a(n) ~ 2^(8*n+1/2) / (sqrt(Pi) * n^(3/2) * 3^(2*n+3/2)). - _Vaclav Kotesovec_, Aug 26 2017

%p a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*8*

%p (4*n-3)*(2*n-1)*(4*n-1)/((3*n-1)*(3*n+1)*n))

%p end:

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Aug 26 2017

%t m = 20; A[_] = 0;

%t Do[A[x_] = 1 + 3 x A[x]^4 + O[x]^m, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 06 2019 *)

%Y Cf. A291285.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Aug 26 2017

%E More terms from _Alois P. Heinz_, Aug 26 2017