cp's OEIS Frontend

A170307 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170307 #10 Jan 30 2025 18:00:01
%S A170307 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A170307 34867844010,313810596090,2824295364810,25418658283290,
%U A170307 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A170307 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170307 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A170307 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170307 <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).
%F A170307 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 A170307 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 A170307 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 A170307 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 A170307 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 A170307 2*t + 1)/(36*t^42 - 8*t^41 - 8*t^40 - 8*t^39 - 8*t^38 - 8*t^37 - 8*t^36
%F A170307 - 8*t^35 - 8*t^34 - 8*t^33 - 8*t^32 - 8*t^31 - 8*t^30 - 8*t^29 - 8*t^28
%F A170307 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22 - 8*t^21 - 8*t^20
%F A170307 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12
%F A170307 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 -
%F A170307 8*t^3 - 8*t^2 - 8*t + 1)
%t A170307 With[{num=Total[2t^Range[41]]+t^42+1,den=Total[-8 t^Range[41]]+36t^42+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 25 2013 *)
%t A170307 coxG[{42,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jan 30 2025 *)
%K A170307 nonn
%O A170307 0,2
%A A170307 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009