cp's OEIS Frontend

A170360 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170360 #8 Nov 21 2016 19:17:57
%S A170360 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170360 309915701760,4338819824640,60743477544960,850408685629440,
%U A170360 11905721598812160,166680102383370240,2333521433367183360
%N A170360 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170360 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170360 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170360 <a href="/index/Rec#order_43">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, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A170360 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170360 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170360 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170360 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170360 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170360 + 2*t^2 + 2*t + 1)/(91*t^43 - 13*t^42 - 13*t^41 - 13*t^40 - 13*t^39 -
%F A170360 13*t^38 - 13*t^37 - 13*t^36 - 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 -
%F A170360 13*t^31 - 13*t^30 - 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 -
%F A170360 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 -
%F A170360 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 -
%F A170360 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 -
%F A170360 13*t^2 - 13*t + 1)
%t A170360 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-13 t^Range[42]]+ 91t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 19 2013 *)
%K A170360 nonn
%O A170360 0,2
%A A170360 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009