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A291096 Number of rooted gluings of octahedra with n square vertices. 2
1, 3, 36, 594, 11340, 235467, 5164236, 117704340, 2760422652, 66179363580, 1614629242512, 39958835859306, 1000667989897524, 25310418084553770, 645671000841035400, 16592979103827051240, 429173117580596633820, 11163550152596460675012, 291848008677713303547312 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 06 2019 *)

CROSSREFS

Cf. A291285.

Sequence in context: A233196 A245114 A276018 * A234869 A305991 A203493

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

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Last modified April 6 18:45 EDT 2020. Contains 333286 sequences. (Running on oeis4.)