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

1,3

Comments

Bisections are A112944 and A113181.

Links

Table of n, a(n) for n=1..28.

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

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 *)

Crossrefs

Cf. A018224, A112944, A113181.

Sequence in context: A296418 A006785 A274538 * A165433 A238728 A271718

Adjacent sequences: A113179 A113180 A113181 * A113183 A113184 A113185

Keyword

nonn

Author

Valery A. Liskovets, Oct 19 2005

Status

approved