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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, Groups et Algèbres 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 Poincaré 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^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+t),

and t2 = (1-t)*(1-t^11)*(1-t^19)*(1-t^29).

MATHEMATICA

CoefficientList[Series[(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^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 + t)/((1 - t)*(1 - t^11)*(1 - t^19)*(1 - t^29)), {t, 0, 50}], t] (* Wesley Ivan Hurt, Apr 12 2017 *)

CROSSREFS

For the growth series for the finite group see A162497.

Sequence in context: A074784 A109678 A000330 * A266784 A211804 A283591

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 May 30 03:33 EDT 2017. Contains 287305 sequences.