cp's OEIS Frontend

A047754 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type H.

%I A047754 #19 Apr 30 2024 07:51:59
%S A047754 0,0,0,0,0,0,0,0,1,0,0,0,5,0,0,0,26,0,0,0,133,0,0,0,708,0,0,0,3861,0,
%T A047754 0,0,21604,0,0,0,123266,0,0,0,715221,0,0,0,4206956,0,0,0,25032840,0,0,
%U A047754 0,150413348,0,0,0,911379384,0,0,0,5562367173,0,0,0,34164355848
%N A047754 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type H.
%C A047754 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 H achiral symmetry and n tetrahedral cells. The axis of symmetry is the line joining the centers of opposite edges of a tetrahedral cell (31); the order of the symmetry group is 4. An achiral polyomino is identical to its reflection. - _Robert A. Russell_, Mar 22 2024
%H A047754 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 A047754 Robert A. Russell, <a href="/A047754/a047754.txt">Mathematica Graphics3D program for A047754 example</a>
%F A047754 If n=4m+1 then (1/2)*(A001764(m) - A047753(n) - A047751(n)), otherwise 0.
%F A047754 G.f.: z * (G(z^4) - G(z^8) - z^4*G(z^8)^2) / 2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - _Robert A. Russell_, Mar 22 2024
%t A047754 Table[If[1==Mod[n,4],Binomial[(3n-3)/4,(n-1)/4]/(n+1)-If[1==Mod[n,8],2Binomial[(3n-3)/8,(n-1)/8],4Binomial[(3n-7)/8,(n-5)/8]]/(n+3),0],{n,40}] (* _Robert A. Russell_, Mar 22 2024 *)
%Y A047754 Cf. A047755.
%Y A047754 Cf. A007173 (oriented), A027610 (unoriented), A371351 (achiral), A001764 (rooted), A047751 (type K), A047753 (type I).
%K A047754 nonn
%O A047754 1,13
%A A047754 _N. J. A. Sloane_