This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047776 #27 Apr 19 2024 04:35:45
%S A047776 0,0,0,0,2,11,71,370,2005,10682,58167,320116,1789210,10121965,
%T A047776 57933469,334919626,1953800059,11489466014,68053583772,405713887061,
%U A047776 2433000197471,14668527134167,88869448492895,540834097467624,3304961431043989,20273201718862728,124798671079300720,770762029389852807
%N A047776 Number of chiral pairs of asymmetric dissectable polyhedra with n tetrahedral cells (type A).
%C A047776 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 asymmetric (type A) with n tetrahedral cells. The order of the symmetry group is 1. Each member of a chiral pair is a reflection but not a rotation of the other. - _Robert A. Russell_, Mar 31 2024
%H A047776 L. W. Beineke and R. E. Pippert, <a href="http://dx.doi.org/10.4153/CJM-1974-006-x">Enumerating dissectable polyhedra by their automorphism groups</a>, Canad. J. Math., 26 (1974), 50-67.
%H A047776 Robert A. Russell, <a href="/A047776/a047776.txt">Mathematica Graphics3D program for A047776 examples</a>
%F A047776 From _Robert A. Russell_, Mar 31 2024: (Start)
%F A047776 a(n) = A001764(n)/(12(n+1)) - A047775(n)/2 - A047774(n)/3 - A047773(n)/6 - A047762(n)/2 - A047760(n)/4 - A047758(n)/4 - A047754(n)/4 - A047753(n)/8 - A047752(n)/12 - A047751(n)/24 - A047771(n)/2 - A047769(n)/2 - A047766(n)/6 - A047766(n)/6 - A047765(n)/4 - A047764(n)/12.
%F A047776 G.f.: (G(z^4) + G(z^6) - 2)/(2z) - z/3 + G(z)/6 - G(z)^2/12 + z*G(z)^4/24 - 7*G(z^2)/12 - 3z*G(z^2)^2/8 - z*G(z^3)/6 - z^2*G(z^3)^2/12 + G(z^4)/2 - z*G(z^4)/6 + (z*G(z^4)^2 + z^2*G(z^4)^2 + z*G(z^6))/2 + z^2*G(z^6)/12 + (z^2*G(z^6)^2 + z^4*G(z^6)^2 - z^2*G(z^12))/2 + z^5*G(z^12)/6 - (z^8*G(z^12)^2 + z^5*G(z^24) + z^17*G(z^24)^2)/2, where G(z) = 1 + z*G(z)^3 is the g.f. for A001764. (End)
%t A047776 Table[If[n < 5, 0, Binomial[3 n, 2 n + 2]/(3 n (n - 1))
%t A047776 - If[OddQ[n], Binomial[3 n/2 - 1/2, n + 1] 3/(n - 1),
%t A047776 7 Binomial[3 n/2, n + 1]/(3 n)]
%t A047776 - Switch[Mod[n, 3], 1, Binomial[n - 1, 2 n/3 + 1/3]/(n - 1), 2,
%t A047776 Binomial[n - 1, 2 n/3 + 2/3]/(n - 2), _, 0]
%t A047776 + Switch[Mod[n, 4], 1, Binomial[3 n/4 - 3/4, n/2 + 1/2] 2/(3 (n - 1))
%t A047776 + Binomial[3 n/4 + 1/4, n/2 + 3/2] 4/(n - 1) +
%t A047776 Binomial[3 n/4 - 3/4, n/2 + 1/2] 4/(n + 3), 2,
%t A047776 Binomial[3 n/4 - 1/2, n/2 + 1] 8/(n - 2), 3,
%t A047776 Binomial[3 n/4 - 1/4, n/2 + 3/2] 12/(n - 3), 0,
%t A047776 Binomial[3 n/4 - 1, n/2 + 1] 12/(n - 4)] +
%t A047776 Switch[Mod[n, 6], 1, Binomial[n/2 - 1/2, n/3 + 2/3] 6/(n - 1), 2,
%t A047776 Binomial[n/2 - 1, n/3 + 1/3] 4/(n - 2) +
%t A047776 Binomial[n/2, n/3 + 4/3] 6/(n - 2) +
%t A047776 Binomial[n/2 - 1, n/3 + 1/3] 6/(n + 4), 4,
%t A047776 Binomial[n/2 - 1, n/3 + 2/3] 12/(n - 4), 5,
%t A047776 Binomial[n/2 - 1/2, n/3 + 1/3] 9/(n + 4), _, 0] +
%t A047776 Switch[Mod[n, 12], 2, -Binomial[n/4 - 1/2, n/6 + 2/3] 12/(n - 2), 5,
%t A047776 Binomial[n/4 - 5/4, n/6 - 5/6] 2/(n + 1),
%t A047776 8, -Binomial[n/4 - 1, n/6 - 1/3] 12/(n + 4), _, 0] -
%t A047776 Switch[Mod[n, 24], 5, Binomial[n/8 - 5/8, n/12 - 5/12] 12/(n + 7), 17,
%t A047776 Binomial[n/8 - 9/8, n/12 - 5/12] 24/(n + 7), _, 0]]/2, {n, 1, 60}] (* _Robert A. Russell_, Apr 09 2012 *)
%Y A047776 Cf. A007173 (oriented), A027610 (unoriented), A371350 (chiral), A001764 (rooted), A047775 (type B), A047774 (type C). A047773 (type D), A047762 (type E), A047760 (type F), A047758 (type G), A047754 (type H), A047753 (type I), A047752 (type J), A047751 (type K), A047771 (type L), A047769 (type M), A047766 (type N|O), A047765 (type P), A047764 (type Q).
%K A047776 nonn,easy
%O A047776 1,5
%A A047776 _N. J. A. Sloane_