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
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-François Alcover, Aug 28 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Mar 17 2005
STATUS
approved