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A169376 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169376 #15 Oct 11 2024 06:58:48
%S A169376 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169376 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169376 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169376 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169376 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169376 First disagreement at index 31: a(31) = 75956370334688139819982767799631231060016801, A170746(31) = 75956370334688139819982767799631231060017152. - _Klaus Brockhaus_, Jun 17 2011
%C A169376 Computed with Magma using commands similar to those used to compute A154638.
%H A169376 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
%F A169376 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)/(325*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
%t A169376 coxG[{31,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 04 2018 *)
%Y A169376 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A169376 nonn
%O A169376 0,2
%A A169376 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009