A374624 a(n) is the number of irreducible finite Coxeter groups in n dimensions, or -1 if there are an infinite number.
1, -1, 3, 5, 3, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
Offset: 1
Examples
For n = 4, there are five finite groups, denoted A(4) (symmetry group of the simplex), B(4) (= C(4)) (symmetry group of the tesseract and the 4-dimensional cross polytope), D(4) (symmetry group of the demitesseract), F(4) (symmetry group of the 24-cell) and H(4) (symmetry group of the 120-cell and the 600-cell).
References
- H. S. M. Coxeter, Regular Polytopes, Dover Publications, Inc., 1973.
Links
- Index entries for linear recurrences with constant coefficients, signature (1).
Programs
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Mathematica
PadRight[{1, -1, 3, 5, 3, 4, 4, 4}, 100, 3] (* Paolo Xausa, Dec 07 2024 *) -
PARI
a(n)=if(n>8,3,[1,-1,3,5,3,4,4,4][n]) \\ Charles R Greathouse IV, Jul 15 2024
Formula
G.f.: (1 - 2*x + 4*x^2 + 2*x^3 - 2*x^4 + x^5 - x^8)/(1 - x). - Stefano Spezia, Jul 15 2024
Comments