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A169379 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169379 #15 Oct 11 2024 06:58:19
%S A169379 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A169379 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A169379 10614443496164071230,307818861388758065670,8926746980273983904430
%N A169379 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169379 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A169379 First disagreement at index 31: a(31) = 2233886953250253687068790546815984030040617595, A170749(31) = 2233886953250253687068790546815984030040618030. - _Klaus Brockhaus_, Jun 17 2011
%C A169379 Computed with Magma using commands similar to those used to compute A154638.
%H A169379 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A169379 G.f.: (t^31 + 2*t^30 + 2*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)/(406*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
%t A169379 coxG[{31,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 08 2015 *)
%Y A169379 Cf. A170749 (G.f.: (1+x)/(1-29*x)).
%K A169379 nonn
%O A169379 0,2
%A A169379 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009