cp's OEIS Frontend

A169578 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169578 #8 Aug 20 2021 11:23:27
%S A169578 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A169578 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A169578 4870003042163884032,175320109517899825152,6311523942644393705472
%N A169578 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169578 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A169578 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169578 <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A169578 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 A169578 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 A169578 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 A169578 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 A169578 + 2*t^2 + 2*t + 1)/(630*t^35 - 35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 -
%F A169578 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 -
%F A169578 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 -
%F A169578 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 -
%F A169578 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 -
%F A169578 35*t + 1)
%t A169578 coxG[{35,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 20 2021 *)
%K A169578 nonn
%O A169578 0,2
%A A169578 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009