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A103937 Number of unrooted n-edge maps in the plane (planar with a distinguished outside face). 0
2, 6, 26, 150, 1032, 8074, 67086, 586752, 5317226, 49592424, 473357994, 4606116310, 45554761836, 456848968518, 4637014782748, 47563495004742, 492422043299964, 5140194991046122, 54053208147441474, 572191817441284272 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.

LINKS

Table of n, a(n) for n=1..20.

V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

FORMULA

a(n)=(1/(2n))[3^n*binomial(2n, n)/(n+1) +sum_{0<k<n, k|n}phi(n/k)3^k*binomial(2k, k)]+q(n) where phi is the Euler function A000010, q(n)=0 if n is even and q(n)=3^((n-1)/2)binomial(n-1, (n-1)/2)/(n+1) if n is odd.

MATHEMATICA

a[n_] := (1/(2n)) (3^n Binomial[2n, n]/(n+1) + Sum[Boole[0<k<n] EulerPhi[ n/k] 3^k Binomial[2k, k], {k, Divisors[n]}]) + q[n];

q[n_] := If[EvenQ[n], 0, 3^((n-1)/2) Binomial[n-1, (n-1)/2]/(n+1)];

Array[a, 20] (* Jean-Fran├žois Alcover, Aug 28 2019 *)

CROSSREFS

Cf. A005159, A005470.

Sequence in context: A052844 A247224 A052859 * A159311 A000629 A185994

Adjacent sequences:  A103934 A103935 A103936 * A103938 A103939 A103940

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Mar 17 2005

STATUS

approved

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Last modified May 17 09:03 EDT 2021. Contains 343969 sequences. (Running on oeis4.)