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A170384 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170384 #8 Dec 22 2024 10:41:42
%S A170384 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170384 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170384 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170384 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170384 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170384 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170384 <a href="/index/Rec#order_43">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, 37, 37, -703).
%F A170384 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170384 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170384 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170384 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170384 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
%F A170384 + 2*t^2 + 2*t + 1)/(703*t^43 - 37*t^42 - 37*t^41 - 37*t^40 - 37*t^39 -
%F A170384 37*t^38 - 37*t^37 - 37*t^36 - 37*t^35 - 37*t^34 - 37*t^33 - 37*t^32 -
%F A170384 37*t^31 - 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 -
%F A170384 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 -
%F A170384 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 -
%F A170384 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 -
%F A170384 37*t^2 - 37*t + 1)
%t A170384 coxG[{43,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 22 2024 *)
%K A170384 nonn
%O A170384 0,2
%A A170384 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009