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A170709 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170709 #26 Nov 19 2016 02:40:14
%S A170709 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170709 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170709 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170709 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170709 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170709 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170709 About the initial comment, first disagreement is at index 50 and the difference is 378. - _Vincenzo Librandi_, Dec 06 2012
%H A170709 Vincenzo Librandi, <a href="/A170709/b170709.txt">Table of n, a(n) for n = 0..200</a>
%H A170709 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A170709 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 A170709 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 A170709 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 A170709 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 A170709 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 A170709 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 A170709 2*t + 1)/(351*t^50 - 26*t^49 - 26*t^48 - 26*t^47 - 26*t^46 - 26*t^45 -
%F A170709 26*t^44 - 26*t^43 - 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 -
%F A170709 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 -
%F A170709 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 -
%F A170709 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 -
%F A170709 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 -
%F A170709 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 -
%F A170709 26*t + 1).
%t A170709 With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-26 t^Range[49]] + 351 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%K A170709 nonn
%O A170709 0,2
%A A170709 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009