A113182 Number of unrooted two-vertex (or, dually, two-face) regular planar maps of valency n considered up to orientation-preserving homeomorphism.

1, 1, 2, 3, 7, 14, 39, 95, 308, 859, 3013, 9130, 33300, 106039, 394340, 1297295, 4878109, 16428300, 62232321, 213388961, 812825244, 2827645453, 10818489817, 38086408002, 146250545528, 520062618300, 2003199281223, 7184570776213

Offset: 1

Author

Valery A. Liskovets, Oct 19 2005

Keywords

• nonn

Comments

Bisections are A112944 and A113181.

Links

• M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar two-face maps, Discrete Math., vol. 222 (2000), 1-25.

Crossrefs

Cf. A018224, A112944, A113181.

Programs

Mathematica

a[n_] := If[OddQ[n], (1/(2n))(Sum[EulerPhi[d] Binomial[2 Floor[(n-1)/(2d)], Floor[(n-1)/(2d)]]^2, {d, Divisors[n]}] + n Binomial[n-1, (n-1)/2]), (1/4)((2 Sum[EulerPhi[d] Binomial[n/d-1, Floor[n/(2d)]]^2, {d, Divisors[ n]}])/n + Binomial[n, n/2])];
Array[a, 28] (* Jean-François Alcover, Aug 30 2019 *)