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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.

%I A112945 #9 Aug 29 2019 05:27:46
%S A112945 0,6,468,80600,16016560,3360790440,728936019504,161858688461184,
%T A112945 36580777518027600,8382066029146609800,1941971956789550319920,
%U A112945 454006489072843947528288,106944132919124515725427808
%N 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.
%H A112945 Z. C. Gao, V. A. Liskovets and N. C. Wormald, <a href="http://mathstat.carleton.ca/~zgao/PAPER/poles.pdf">Enumeration of unrooted odd-valent regular planar maps</a>, Preprint, 2005; Annals of Combinatorics, August 2009, Volume 13, Issue 2, pp 233-259.
%F A112945 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.
%t A112945 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];
%t A112945 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Aug 29 2019 *)
%Y A112945 Cf. A112944, A112946.
%K A112945 nonn
%O A112945 0,2
%A A112945 _Valery A. Liskovets_, Oct 10 2005