OFFSET
1,6
COMMENTS
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 M chiral symmetry and n tetrahedral cells. The axis of symmetry is the altitude of a tetrahedral face (21); the order of the symmetry group is 2. An achiral polyomino is identical to its reflection. - Robert A. Russell, Mar 22 2024
LINKS
L. W. Beineke and R. E. Pippert, Enumerating dissectable polyhedra by their automorphism groups, Canad. J. Math., 26 (1974), 50-67.
Robert A. Russell, Mathematica Graphics3D program for A047769 example
FORMULA
MATHEMATICA
Table[If[OddQ[n], 0, (Binomial[3n/2, n/2]/(n+1)-If[0==Mod[n, 4], 2Binomial[3n/4, n/4]/(n+2), 4Binomial[(3n-2)/4, (n-2)/4]/(n+2), 0]- If[2==Mod[n, 6], 3Binomial[3(n-2)/6, (n-2)/6]/(n+1)- If[2==Mod[n, 12], 6Binomial[3(n-2)/12, (n-2)/12], 12Binomial[(3n-12)/12,
(n-8)/12]]/(n+4), 0])/2], {n, 60}] (* Robert A. Russell, Mar 22 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved