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 A047765 #19 Apr 27 2024 03:37:11
%S A047765 0,0,0,1,0,2,0,2,0,7,0,12,0,29,0,55,0,143,0,271,0,728,0,1428,0,3873,0,
%T A047765 7752,0,21318,0,43256,0,120175,0,246675,0,690678,0,1430715,0,4032015,
%U A047765 0,8414610,0,23841480,0,50067108,0,142498637,0,300830572
%N A047765 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type P.
%C A047765 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 P achiral symmetry and n tetrahedral cells. The center of symmetry is the altitude of a tetrahedral face (21); the order of the symmetry group is 4. An achiral polyomino is identical to its reflection. - _Robert A. Russell_, Mar 22 2024
%H A047765 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 A047765 Robert A. Russell, <a href="/A047765/a047765.txt">Mathematica Graphics3D program for A047765 examples</a>
%F A047765 If n=2m then A047749(m) - A047764(n), otherwise 0.
%F A047765 G.f.: G(z^4) + z^2*G(z^4)^2 - z^2*G(z^12) - z^8*G(z^12)^2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - _Robert A. Russell_, Mar 22 2024
%t A047765 Table[If[OddQ[n],0,If[OddQ[n/2],2Binomial[(3n-2)/4,(n-2)/4],Binomial[3n/4,n/4]]/(n/2+1)-Switch[Mod[n,12],2,6Binomial[(n-2)/4,(n-2)/12],8,12Binomial[(n-4)/4,(n-2)/6],_,0]/(n+4)],{n,52}] (* _Robert A. Russell_, Mar 22 2024 *)
%Y A047765 Cf. A047767.
%Y A047765 Cf. A007173 (oriented), A027610 (unoriented), A371351 (achiral), A001764 (rooted), A047749 (type U), A047764 (type Q).
%K A047765 nonn
%O A047765 1,6
%A A047765 _N. J. A. Sloane_