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A170288 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170288 #8 Jun 12 2022 15:29:26
%S A170288 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170288 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170288 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170288 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170288 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170288 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170288 <a href="/index/Rec#order_41">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, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
%F A170288 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170288 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170288 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170288 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170288 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 +
%F A170288 1)/(703*t^41 - 37*t^40 - 37*t^39 - 37*t^38 - 37*t^37 - 37*t^36 - 37*t^35
%F A170288 - 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 - 37*t^29 - 37*t^28 -
%F A170288 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 -
%F A170288 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 -
%F A170288 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 -
%F A170288 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
%t A170288 coxG[{41,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2022 *)
%K A170288 nonn
%O A170288 0,2
%A A170288 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009