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A169290 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169290 #12 Dec 25 2024 13:09:38
%S A169290 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A169290 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A169290 4870003042163884032,175320109517899825152,6311523942644393705472
%N A169290 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169290 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A169290 First disagreement at index 29: a(29) = 1395313337411653184494553884359305820238773606, A170756(29) = 1395313337411653184494553884359305820238774272. - _Klaus Brockhaus_, Jun 03 2011
%C A169290 Computed with Magma using commands similar to those used to compute A154638.
%H A169290 <a href="/index/Rec#order_29">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, -630).
%F A169290 G.f.: (t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(630*t^29 - 35*t^28 - 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).
%t A169290 coxG[{29,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 25 2024 *)
%Y A169290 Cf. A170756 (G.f.: (1+x)/(1-36*x)).
%K A169290 nonn
%O A169290 0,2
%A A169290 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009