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A170432 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170432 #8 Aug 23 2017 16:20:41
%S A170432 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170432 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170432 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170432 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170432 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170432 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170432 <a href="/index/Rec#order_44">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, 37, -703).
%F A170432 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170432 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170432 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170432 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170432 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
%F A170432 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^44 - 37*t^43 - 37*t^42 - 37*t^41 -
%F A170432 37*t^40 - 37*t^39 - 37*t^38 - 37*t^37 - 37*t^36 - 37*t^35 - 37*t^34 -
%F A170432 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 - 37*t^29 - 37*t^28 - 37*t^27 -
%F A170432 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 - 37*t^22 - 37*t^21 - 37*t^20 -
%F A170432 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 - 37*t^15 - 37*t^14 - 37*t^13 -
%F A170432 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5
%F A170432 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1)
%t A170432 coxG[{44,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 23 2017 *)
%K A170432 nonn
%O A170432 0,2
%A A170432 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009