cp's OEIS Frontend

A170005 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170005 #8 Feb 23 2022 18:16:06
%S A170005 1,44,1892,81356,3498308,150427244,6468371492,278139974156,
%T A170005 11960018888708,514280812214444,22114074925221092,950905221784506956,
%U A170005 40888924536733799108,1758223755079553361644,75603621468420794550692
%N A170005 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170005 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A170005 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170005 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).
%F A170005 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 A170005 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 A170005 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 A170005 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 A170005 + 2*t^2 + 2*t + 1)/(903*t^35 - 42*t^34 - 42*t^33 - 42*t^32 - 42*t^31 -
%F A170005 42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 -
%F A170005 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 -
%F A170005 42*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*t^12 - 42*t^11 - 42*t^10 -
%F A170005 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 -
%F A170005 42*t + 1)
%t A170005 coxG[{35,903,-42}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 23 2022 *)
%K A170005 nonn
%O A170005 0,2
%A A170005 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009