A112945 Number of unrooted regular odd-valent planar maps with 4 vertices; maps are considered up to orientation-preserving homeomorphisms and the vertices are of valency 2n+1.

0, 6, 468, 80600, 16016560, 3360790440, 728936019504, 161858688461184, 36580777518027600, 8382066029146609800, 1941971956789550319920, 454006489072843947528288, 106944132919124515725427808

Offset: 0

Author

Valery A. Liskovets, Oct 10 2005

Keywords

• nonn

Links

• Z. C. Gao, V. A. Liskovets and N. C. Wormald, Enumeration of unrooted odd-valent regular planar maps, Preprint, 2005; Annals of Combinatorics, August 2009, Volume 13, Issue 2, pp 233-259.

Crossrefs

Cf. A112944, A112946.

Programs

Mathematica

a[n_] := (n/6) Binomial[2n, n]^4 + (n/2) Binomial[2n, n]^2 + (2/3) Boole[ Divisible[2n+1, 3]] Binomial[2 Floor[n/3], Floor[n/3]] Binomial[2n, n];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Aug 29 2019 *)

Formula

a(n) = (n/6)*binomial(2n, n)^4+(n/2)*binomial(2n, n)^2+(2/3)*delta(3|(2n+1))* binomial(2*floor(n/3), floor(n/3))*binomial(2n, n) where delta(3|(2n+1))=1 if 3|(2n+1) and =0 otherwise.