cp's OEIS Frontend

A170714 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

%I A170714 #24 Nov 18 2016 18:11:02
%S A170714 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A170714 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A170714 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A170714 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
%C A170714 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A170714 Computed with MAGMA using commands similar to those used to compute A154638.
%C A170714 About the initial comment, first disagreement is at index 50 and the difference is 528.  - _Vincenzo Librandi_, Dec 06 2012
%H A170714 Vincenzo Librandi, <a href="/A170714/b170714.txt">Table of n, a(n) for n = 0..200</a>
%H A170714 <a href="/index/Rec#order_50">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A170714 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 A170714 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 A170714 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 A170714 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 A170714 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 A170714 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 A170714 2*t + 1)/(496*t^50 - 31*t^49 - 31*t^48 - 31*t^47 - 31*t^46 - 31*t^45 -
%F A170714 31*t^44 - 31*t^43 - 31*t^42 - 31*t^41 - 31*t^40 - 31*t^39 - 31*t^38 -
%F A170714 31*t^37 - 31*t^36 - 31*t^35 - 31*t^34 - 31*t^33 - 31*t^32 - 31*t^31 -
%F A170714 31*t^30 - 31*t^29 - 31*t^28 - 31*t^27 - 31*t^26 - 31*t^25 - 31*t^24 -
%F A170714 31*t^23 - 31*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 -
%F A170714 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 -
%F A170714 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 -
%F A170714 31*t + 1).
%t A170714 With[{num = Total[2 t^Range[49]]+ t^50 + 1,den = Total[-31  t^Range[49]] + 496 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* _Vincenzo Librandi_, Dec 06 2012 *)
%K A170714 nonn
%O A170714 0,2
%A A170714 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009