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URL: https://oeis.org/A291096

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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
OFFSET
0,2
LINKS
Valentin Bonzom and 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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 26 2017
EXTENSIONS
More terms from Alois P. Heinz, Aug 26 2017
STATUS
approved