cp's OEIS Frontend

A047751 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type K.

%I A047751 #17 Mar 31 2024 14:03:28
%S A047751 1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T A047751 0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,7,0,0,0,
%U A047751 0,0,0,0,0,0,0,0,12,0,0,0,0,0,0,0,0,0,0,0,30,0,0
%N A047751 Number of dissectable polyhedra with n tetrahedral cells and symmetry of type K.
%C A047751 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 K achiral symmetry and n tetrahedral cells. The center of symmetry is the center of a tetrahedral cell (3); the order of the symmetry group is 24. An achiral polyomino is identical to its reflection. - _Robert A. Russell_, Mar 22 2024
%H A047751 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 A047751 Robert A. Russell, <a href="/A047751/a047751.txt">Mathematica Graphics3D program for A047751 examples</a>
%F A047751 a(1)=1, a(n)=0 unless n == 5 (mod 12); a(12m+5) = A047749(m).
%F A047751 G.f.: z + z^5*G(z^24) + z^17*G(z^24)^2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - _Robert A. Russell_, Mar 22 2024
%t A047751 Table[Boole[1==n]+Switch[Mod[n,24],5,12Binomial[(n-5)/8,(n-5)/12],17,24Binomial[(n-9)/8,(n-17)/24],_,0]/(n+7),{n,60}] (* _Robert A. Russell_, Mar 22 2024 *)
%Y A047751 Cf. A007173 (oriented), A027610 (unoriented), A371351 (achiral), A001764 (rooted).
%K A047751 nonn
%O A047751 1,41
%A A047751 _N. J. A. Sloane_