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A169388 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169388 #16 Apr 21 2025 12:09:34
%S A169388 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A169388 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A169388 9304309958718547968,353563778431304822784,13435423580389583265792
%N A169388 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169388 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A169388 First disagreement at index 31: a(31) = 9651004220209771952794467740675318224269959232795, A170758(31) = 9651004220209771952794467740675318224269959233536. - _Klaus Brockhaus_, Jun 17 2011
%C A169388 Computed with Magma using commands similar to those used to compute A154638.
%H A169388 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A169388 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)/(703*t^31 - 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
%t A169388 coxG[{31,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 21 2025 *)
%Y A169388 Cf. A170758 (G.f.: (1+x)/(1-38*x)).
%K A169388 nonn
%O A169388 0,2
%A A169388 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009