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A170706 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170706 #21 Mar 15 2024 03:47:44
%S A170706 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A170706 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A170706 913008685901414400,21912208461633945600,525893003079214694400
%N A170706 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170706 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A170706 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170706 About the initial comment, first disagreement is at index 50 and the difference is 300. - _Vincenzo Librandi_, Dec 06 2012
%H A170706 Vincenzo Librandi, <a href="/A170706/b170706.txt">Table of n, a(n) for n = 0..200</a>
%H A170706 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
%F A170706 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 A170706 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 A170706 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 A170706 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 A170706 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 A170706 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 A170706 2*t + 1)/(276*t^50 - 23*t^49 - 23*t^48 - 23*t^47 - 23*t^46 - 23*t^45 -
%F A170706 23*t^44 - 23*t^43 - 23*t^42 - 23*t^41 - 23*t^40 - 23*t^39 - 23*t^38 -
%F A170706 23*t^37 - 23*t^36 - 23*t^35 - 23*t^34 - 23*t^33 - 23*t^32 - 23*t^31 -
%F A170706 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 -
%F A170706 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 -
%F A170706 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 -
%F A170706 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 -
%F A170706 23*t + 1).
%t A170706 With[{num=Total[2 t^Range[49]] + t^50 + 1, den=Total[-23 t^Range[49]] + 276 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%K A170706 nonn
%O A170706 0,2
%A A170706 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009