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%I #5 Mar 21 2024 08:32:06
%S 0,0,0,0,1,10,80,611,4602,34791,265606,2054034,16094883,127693729,
%T 1024649237,8306343347,67952829212,560471786912,4656785469564,
%U 38948533963500,327715193729107,2772468576820531
%N Number of chiral pairs of polyominoes composed of n pentachoral cells of the hyperbolic regular tiling with Schläfli symbol {3,3,3,oo}.
%C Also number of chiral pairs of simplicial 4-clusters or stack polytopes with n pentachoral cells. Each member of a chiral pair is a reflection but not a rotation of the other. Some of the h(4,n) terms in the Hering article are in error, including the 6th, 8th and 9th.
%H F. Hering et al., <a href="http://dx.doi.org/10.1016/0012-365X(82)90121-2">The enumeration of stack polytopes and simplicial clusters</a>, Discrete Math., 40 (1982), 203-217.
%F a(n) = A007175(n) - A182322(n) = (A007175(n) - A182299(n))/2 = A182322(n) - A182299(n).
%F a(n) = h(4,n) - H(4,n) in Table 8 of Hering link.
%Y Cf. A007175 (oriented), A182322 (oriented), A182299 (achiral), A002293 (rooted), A371350 {3,3,oo}.
%Y This is the half the difference of A007175 and A182299, both of which have Mathematica programs.
%K nonn
%O 1,6
%A _Robert A. Russell_, Mar 20 2024
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