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%I #15 Mar 22 2024 17:02:29
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
%T 0,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,26,0,0,0,0,0,0,0,0,0,0,0,133,0,0,
%U 0,0,0,0,0,0,0,0,0,708,0,0,0,0,0,0,0,0,0,0,0,3861,0
%N Number of chiral pairs of dissectable polyhedra with n tetrahedral cells and symmetry of type J.
%C One of 17 different symmetry types comprising A007173 and A027610 and one of 7 for A371350. Also the number of tetrahedral clusters or polyominoes of the regular tiling with Schläfli symbol {3,3,oo}, both having type J chiral symmetry and n tetrahedral cells. The center of symmetry is the center of a tetrahedral cell (3); the order of the symmetry group is 12. Each member of a chiral pair is a reflection but not a rotation of the other. - _Robert A. Russell_, Mar 22 2024
%H 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.
%F If n=12m+5 then (1/2)*(A001764(m) - A047751(n)), otherwise 0.
%F G.f.: z^5 * (G(z^12) - G(z^24) - z^12*G(z^24)^2) / 2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - _Robert A. Russell_, Mar 22 2024
%t Table[Switch[Mod[n,24],5,6Binomial[(n-5)/4,(n-5)/12]/(n+1)-12Binomial[(n-5)/8,(n-5)/12]/(n+7),17,6Binomial[(n-5)/4,(n-5)/12]/(n+1)-24Binomial[(n-9)/8,(n-17)/24]/(n+7),_,0]/2,{n,60}] (* _Robert A. Russell_, Mar 22 2024 *)
%Y Cf. A007173 (oriented), A027610 (unoriented), A371350 (chiral), A001764 (rooted), A047751 (type K).
%K nonn
%O 1,41
%A _N. J. A. Sloane_
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