A291096 Number of rooted gluings of octahedra with n square vertices.

1, 3, 36, 594, 11340, 235467, 5164236, 117704340, 2760422652, 66179363580, 1614629242512, 39958835859306, 1000667989897524, 25310418084553770, 645671000841035400, 16592979103827051240, 429173117580596633820, 11163550152596460675012, 291848008677713303547312

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..691

Valentin Bonzom, Luca Lionni, Counting Gluings of Octahedra, Electronic Journal of Combinatorics 24(3) (2017), #P3.36.

Formula

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

a(n) ~ 2^(8*n+1/2) / (sqrt(Pi) * n^(3/2) * 3^(2*n+3/2)). - Vaclav Kotesovec, Aug 26 2017

Maple

a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*8*
      (4*n-3)*(2*n-1)*(4*n-1)/((3*n-1)*(3*n+1)*n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 26 2017

Mathematica

m = 20; A[_] = 0;
Do[A[x_] = 1 + 3 x A[x]^4 + O[x]^m, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 06 2019 *)

Crossrefs

Cf. A291285.

Sequence in context: A368048 A245114 A276018 * A234869 A371660 A305991

Adjacent sequences: A291093 A291094 A291095 * A291097 A291098 A291099

Keyword

nonn

Author

N. J. A. Sloane, Aug 26 2017

Extensions

More terms from Alois P. Heinz, Aug 26 2017

Status

approved