OFFSET
1,41
COMMENTS
One of 17 different symmetry types comprising A007173 and A027610 and one of 10 for A371351. Also the number of tetrahedral clusters or polyominoes of the regular tiling with Schläfli symbol {3,3,oo}, both having type K achiral symmetry and n tetrahedral cells. The center of symmetry is the center of a tetrahedral cell (3); the order of the symmetry group is 24. 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 A047751 examples
FORMULA
a(1)=1, a(n)=0 unless n == 5 (mod 12); a(12m+5) = A047749(m).
G.f.: z + z^5*G(z^24) + z^17*G(z^24)^2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. - Robert A. Russell, Mar 22 2024
MATHEMATICA
Table[Boole[1==n]+Switch[Mod[n, 24], 5, 12Binomial[(n-5)/8, (n-5)/12], 17, 24Binomial[(n-9)/8, (n-17)/24], _, 0]/(n+7), {n, 60}] (* Robert A. Russell, Mar 22 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved