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A168814
Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
1
1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170760, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 2817498546175999999999999999180, A170760(19) = 2817498546176000000000000000000. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
FORMULA
G.f.:co.
MATHEMATICA
CoefficientList[Series[(t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 17 2016 *)
coxG[{19, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 28 2019 *)
CROSSREFS
Cf. A170760 (G.f.: (1+x)/(1-40*x)).
Sequence in context: A167830 A168718 A168766 * A168862 A168910 A168958
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved