OFFSET
1,17
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 G chiral symmetry and n tetrahedral cells. The axis of symmetry is a line connecting the centers of opposite edges of a tetrahedral cell (31); the order of the symmetry group is 4. Each member of a chiral pair is a reflection but not a rotation of the other. - 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 A047758 example
FORMULA
MATHEMATICA
Table[If[1==Mod[n, 4], (2Boole[1==n]+2Binomial[(3n-3)/4, (n-1)/4]/(n+1)-If[1==Mod[n, 8], 12Binomial[(3n-3)/8, (n-1)/8]/(n+3), 12Binomial[(3n-7)/8, (n+3)/8]/(n-1)]-If[5==Mod[n, 12], 6Binomial[(n-5)/4, (n-5)/12]/(n+1)-If[5==Mod[n, 24], 36Binomial[(n-5)/8, (n-5)/12], 72Binomial[(n-9)/8, (n-17)/24]]/(n+7), 0])/6, 0], {n, 50}] (* Robert A. Russell, Mar 22 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved