A369474 Number of chiral pairs of polyominoes composed of n pentachoral cells of the hyperbolic regular tiling with Schläfli symbol {3,3,3,oo}.

0, 0, 0, 0, 1, 10, 80, 611, 4602, 34791, 265606, 2054034, 16094883, 127693729, 1024649237, 8306343347, 67952829212, 560471786912, 4656785469564, 38948533963500, 327715193729107, 2772468576820531

Offset: 1

Author

Robert A. Russell, Mar 20 2024

Keywords

• nonn

Comments

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.

Links

• F. Hering et al., The enumeration of stack polytopes and simplicial clusters, Discrete Math., 40 (1982), 203-217.

Crossrefs

Cf. A007175 (oriented), A182322 (oriented), A182299 (achiral), A002293 (rooted), A371350 {3,3,oo}.

This is the half the difference of A007175 and A182299, both of which have Mathematica programs.

Formula

a(n) = A007175(n) - A182322(n) = (A007175(n) - A182299(n))/2 = A182322(n) - A182299(n).

a(n) = h(4,n) - H(4,n) in Table 8 of Hering link.