cp's OEIS Frontend

A162495 Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.

%I A162495 #18 Feb 16 2025 08:33:11
%S A162495 1,3,5,7,9,11,12,12,12,12,11,9,7,5,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A162495 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A162495 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A162495 Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.
%C A162495 This group is also the Weyl group H_3.
%C A162495 If the 0's are omitted, this is the coordination sequence for the truncated icosidodecahedron (see Karzes link).
%C A162495 Sometimes "great rhombicosidodecahedron" is preferred when referring in particular to the Archimedean polyhedron with this coordination sequence. - _Peter Munn_, Mar 22 2021
%D A162495 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.
%D A162495 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D A162495 David Wells, Archimedean polyhedra in Penguin Dictionary of Curious and Interesting Geometry, Penguin Books, 1991, pp. 6-7.
%H A162495 Tom Karzes, <a href="/A298808/a298808.html">Polyhedron Coordination Sequences</a>
%H A162495 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatRhombicosidodecahedron.html">Great Rhombicosidodecahedron</a>
%H A162495 <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>
%F A162495 G.f.: (1-x^2)*(1-x^6)*(1-x^10)/(1-x)^3.
%o A162495 (Magma) G := CoxeterGroup(GrpFPCox, "H3");
%o A162495 f := GrowthFunction(G);
%o A162495 Coefficients(f);
%Y A162495 Cf. A161409, A162493, A162494, A162496, A162497.
%K A162495 nonn,fini
%O A162495 0,2
%A A162495 _John Cannon_ and _N. J. A. Sloane_, Dec 01 2009