cp's OEIS Frontend

A169508 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169508 #8 Nov 26 2016 07:33:31
%S A169508 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A169508 309915701760,4338819824640,60743477544960,850408685629440,
%U A169508 11905721598812160,166680102383370240,2333521433367183360
%N A169508 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169508 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A169508 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169508 <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A169508 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169508 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 A169508 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 A169508 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 A169508 2*t + 1)/(91*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 -
%F A169508 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 -
%F A169508 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 -
%F A169508 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 -
%F A169508 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1)
%t A169508 With[{num=Total[2t^Range[33]]+t^34+1,den=Total[-13 t^Range[33]]+ 91t^34+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 16 2012 *)
%K A169508 nonn
%O A169508 0,2
%A A169508 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009