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 A266783 The growth series for the affine Coxeter (or Weyl) group [3,3,5] (or H_4). 1
 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 651, 823, 1024, 1256, 1521, 1821, 2158, 2534, 2952, 3415, 3925, 4485, 5098, 5766, 6491, 7275, 8120, 9028, 10002, 11046, 12162, 13351, 14616, 15960, 17385, 18893, 20486, 22167, 23939, 25805, 27768, 29829, 31989, 34251, 36618, 39092, 41675, 44370, 47180, 50106, 53150, 56315, 59602, 63012 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. Bourbaki, Groupes et AlgĂ¨bres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t). H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under PoincarĂ© polynomial; also Table 3.1 page 59. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA G.f. = t1/t2 where t1 is (1 + t)*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11)*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19)*(1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + t^20 + t^21 + t^22 + t^23 + t^24 + t^25 + t^26 + t^27 + t^28 + t^29) and t2 = (1 - t)*(1 - t^11)*(1 - t^19)*(1 - t^29). G.f.: (1 - x^2)*(1 - x^12)*(1 - x^20)*(1 - x^30)/((1 - x)^5*(1 - x^11)*(1 - x^19)*(1 - x^29)). - G. C. Greubel, Feb 04 2020 MAPLE m:=60; S:=series((1-x^2)*(1-x^12)*(1-x^20)*(1-x^30)/((1-x)^5*(1-x^11)*(1-x^19)*(1-x^29)), x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Feb 04 2020 MATHEMATICA CoefficientList[Series[(1 + t)^4 * (1 + t^2) * (1 + t^2 + t^4) * (1 + t^4 + t^8) * (1 + t^2 + t^4 + t^6 + t^8) * (1 + t^6 + t^10 + t^12 + t^16 + t^18 + t^22 + t^24 + t^28 + t^34)/((1 - t) * (1 - t^11) * (1 - t^19) * (1 - t^29)), {t, 0, 60}], t] (* Wesley Ivan Hurt, Apr 12 2017; modified by G. C. Greubel, Feb 04 2020 *) PROG (PARI) Vec( (1-x^2)*(1-x^12)*(1-x^20)*(1-x^30)/((1-x)^5*(1-x^11)*(1-x^19)*(1-x^29)) +O('x^60) ) \\ G. C. Greubel, Feb 04 2020 (MAGMA) R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^2)*(1-x^12)*(1-x^20)*(1-x^30)/((1-x)^5*(1-x^11)*(1-x^19)*(1-x^29)) )); // G. C. Greubel, Feb 04 2020 (Sage) def A266783_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( (1-x^2)*(1-x^12)*(1-x^20)*(1-x^30)/((1-x)^5*(1-x^11)*(1-x^19)*(1-x^29)) ).list() A266783_list(60) # G. C. Greubel, Feb 04 2020 CROSSREFS For the growth series for the finite group see A162497. Sequence in context: A074784 A109678 A000330 * A266784 A299902 A299899 Adjacent sequences:  A266780 A266781 A266782 * A266784 A266785 A266786 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 11 2016 STATUS approved

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Last modified February 26 09:39 EST 2020. Contains 332277 sequences. (Running on oeis4.)