cp's OEIS Frontend

A169530 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169530 #8 Apr 27 2018 19:04:35
%S A169530 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A169530 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A169530 4870003042163884032,175320109517899825152,6311523942644393705472
%N A169530 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169530 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A169530 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169530 <a href="/index/Rec#order_34">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, -630).
%F A169530 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169530 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169530 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169530 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A169530 2*t + 1)/(630*t^34 - 35*t^33 - 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 -
%F A169530 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 -
%F A169530 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 -
%F A169530 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 -
%F A169530 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1)
%t A169530 coxG[{34,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 27 2018 *)
%K A169530 nonn
%O A169530 0,2
%A A169530 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009