cp's OEIS Frontend

A170002 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A170002 #8 Aug 11 2025 12:56:46
%S A170002 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T A170002 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U A170002 17196646400000000000,687865856000000000000,27514634240000000000000
%N A170002 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A170002 The initial terms coincide with those of A170760, although the two sequences are eventually different.
%C A170002 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170002 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).
%F A170002 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 A170002 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 A170002 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 A170002 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 A170002 + 2*t^2 + 2*t + 1)/(780*t^35 - 39*t^34 - 39*t^33 - 39*t^32 - 39*t^31 -
%F A170002 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27 - 39*t^26 - 39*t^25 - 39*t^24 -
%F A170002 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 - 39*t^19 - 39*t^18 - 39*t^17 -
%F A170002 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 - 39*t^12 - 39*t^11 - 39*t^10 -
%F A170002 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5 - 39*t^4 - 39*t^3 - 39*t^2 -
%F A170002 39*t + 1)
%t A170002 coxG[{35,780,-39}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 11 2025 *)
%K A170002 nonn
%O A170002 0,2
%A A170002 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009