cp's OEIS Frontend

A170312 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170312 #11 Aug 19 2025 12:04:40
%S A170312 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170312 309915701760,4338819824640,60743477544960,850408685629440,
%U A170312 11905721598812160,166680102383370240,2333521433367183360
%N A170312 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170312 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170312 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170312 <a href="/index/Rec#order_42">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, -91).
%F A170312 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170312 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 A170312 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 A170312 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 A170312 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 A170312 2*t + 1)/(91*t^42 - 13*t^41 - 13*t^40 - 13*t^39 - 13*t^38 - 13*t^37 -
%F A170312 13*t^36 - 13*t^35 - 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 -
%F A170312 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 -
%F A170312 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 -
%F A170312 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 -
%F A170312 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1)
%t A170312 With[{num=Total[2t^Range[41]]+t^42+1,den=Total[-13 t^Range[41]]+ 91t^42+1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Oct 11 2011 *)
%t A170312 coxG[{42,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 19 2025 *)
%K A170312 nonn
%O A170312 0,2
%A A170312 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009