cp's OEIS Frontend

A170003 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170003 #9 Nov 26 2016 09:35:03
%S A170003 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170003 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170003 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170003 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170003 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170003 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170003 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170003 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170003 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 A170003 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 A170003 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 A170003 + 2*t^2 + 2*t + 1)/(820*t^35 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 -
%F A170003 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 -
%F A170003 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 -
%F A170003 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 -
%F A170003 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 -
%F A170003 40*t + 1)
%t A170003 With[{num=Total[2t^Range[34]]+t^35+1,den=Total[-40 t^Range[34]]+ 820t^35+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Oct 10 2011 *)
%K A170003 nonn
%O A170003 0,2
%A A170003 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009