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A170729 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170729 #11 Jul 07 2024 13:15:06
%S A170729 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A170729 24317909782224,1142941759764528,53718262708932816,
%U A170729 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A170729 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170729 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A170729 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170729 About the initial comment, first disagreement is at index 50 and the difference is 1128.  - _Vincenzo Librandi_, Dec 08 2012
%H A170729 Vincenzo Librandi, <a href="/A170729/b170729.txt">Table of n, a(n) for n = 0..200</a>
%H A170729 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1080).
%F A170729 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 A170729 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 A170729 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 A170729 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 A170729 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 A170729 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 A170729 2*t + 1)/(1081*t^50 - 46*t^49 - 46*t^48 - 46*t^47 - 46*t^46 - 46*t^45 -
%F A170729 46*t^44 - 46*t^43 - 46*t^42 - 46*t^41 - 46*t^40 - 46*t^39 - 46*t^38 -
%F A170729 46*t^37 - 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 - 46*t^32 - 46*t^31 -
%F A170729 46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 -
%F A170729 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 -
%F A170729 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 -
%F A170729 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 -
%F A170729 46*t + 1)
%t A170729 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-46 t^Range[49]] + 1081 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 08 2012 *)
%t A170729 coxG[{50,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 07 2024 *)
%K A170729 nonn
%O A170729 0,2
%A A170729 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009