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A170719 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170719 #14 Nov 18 2016 18:02:58
%S A170719 1,38,1406,52022,1924814,71218118,2635070366,97497603542,
%T A170719 3607411331054,133474219248998,4938546112212926,182726206151878262,
%U A170719 6760869627619495694,250152176221921340678,9255630520211089605086
%N A170719 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170719 The initial terms coincide with those of A170757, although the two sequences are eventually different.
%C A170719 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170719 About the initial comment, first disagreement is at index 50 and the difference is 703.  - _Vincenzo Librandi_, Dec 06 2012
%H A170719 Vincenzo Librandi, <a href="/A170719/b170719.txt">Table of n, a(n) for n = 0..200</a>
%H A170719 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).
%F A170719 G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
%F A170719 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170719 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170719 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170719 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170719 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 +
%F A170719 2*t + 1)/(666*t^50 - 36*t^49 - 36*t^48 - 36*t^47 - 36*t^46 - 36*t^45 -
%F A170719 36*t^44 - 36*t^43 - 36*t^42 - 36*t^41 - 36*t^40 - 36*t^39 - 36*t^38 -
%F A170719 36*t^37 - 36*t^36 - 36*t^35 - 36*t^34 - 36*t^33 - 36*t^32 - 36*t^31 -
%F A170719 36*t^30 - 36*t^29 - 36*t^28 - 36*t^27 - 36*t^26 - 36*t^25 - 36*t^24 -
%F A170719 36*t^23 - 36*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 -
%F A170719 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 -
%F A170719 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 -
%F A170719 36*t + 1)
%t A170719 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-36  t^Range[49]] + 666 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%K A170719 nonn
%O A170719 0,2
%A A170719 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009