cp's OEIS Frontend

A170006 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170006 #8 Sep 09 2017 10:22:37
%S A170006 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A170006 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A170006 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A170006 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170006 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A170006 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170006 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A170006 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 A170006 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 A170006 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 A170006 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 A170006 + 2*t^2 + 2*t + 1)/(946*t^35 - 43*t^34 - 43*t^33 - 43*t^32 - 43*t^31 -
%F A170006 43*t^30 - 43*t^29 - 43*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 -
%F A170006 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 -
%F A170006 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 -
%F A170006 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 -
%F A170006 43*t + 1)
%t A170006 coxG[{35,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 09 2017 *)
%K A170006 nonn
%O A170006 0,2
%A A170006 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009