This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047771 #27 Apr 28 2024 09:50:36
%S A047771 0,0,0,0,0,1,0,8,0,42,0,232,0,1277,0,7183,0,41041,0,238315,0,1402076,
%T A047771 0,8343804,0,50136483,0,303790544,0,1854115285,0,11388104153,0,
%U A047771 70338364135,0,436605050440,0,2722153369473,0,17040017600925,0
%N A047771 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type L.
%C A047771 One of 17 different symmetry types comprising A007173 and A027610 and one of 10 for A371351. Also the number of tetrahedral clusters or polyominoes of the regular tiling with Schläfli symbol {3,3,oo}, both having type L achiral symmetry and n tetrahedral cells. The plane of symmetry is a tetrahedral face (210); the order of the symmetry group is 2. An achiral polyomino is identical to its reflection. - _Robert A. Russell_, Mar 22 2024
%H A047771 L. W. Beineke and R. E. Pippert, <a href="http://dx.doi.org/10.4153/CJM-1974-006-x">Enumerating dissectable polyhedra by their automorphism groups</a>, Canad. J. Math., 26 (1974), 50-67.
%H A047771 Robert A. Russell, <a href="/A047771/a047771.txt">Mathematica Graphics3D program for A047771 example</a>.
%F A047771 If n=2m then (1/6)*(A001764(m) - 2*A047766(n) - 3*A047765(n) - A047764(n)), otherwise 0.
%F A047771 G.f.: (2 + G(z^2) - z^2*G(z^6)) / 6 - (G(z^4) + z^2*G(z^4)^2 - z^2*G(z^12) - z^8*G(z^12)^2) / 2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - _Robert A. Russell_, Mar 30 2024
%t A047771 Table[(If[OddQ[n],0,Binomial[3n/2,n/2]/(n+1)-6If[OddQ[n/2],2Binomial[(3n-2)/4,(n-2)/4],Binomial[3n/4,n/4]]/(n+2)]-3If[2==Mod[n,6],Binomial[3(n-2)/6,(n-2)/6]/(n+1)-If[2==Mod[n,12],6Binomial[3(n-2)/12,(n-2)/12],12Binomial[n/4-1,(n-8)/12]]/(n+4),0])/6,{n,30}] (* _Robert A. Russell_, Mar 22 2024 *)
%Y A047771 Cf. A047772.
%Y A047771 Cf. A007173 (oriented), A027610 (unoriented), A371351 (achiral), A001764 (rooted), A047764 (type Q), A047765 (type P), A047766 (type N).
%K A047771 nonn
%O A047771 1,8
%A A047771 _N. J. A. Sloane_