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A170336 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170336 #8 Sep 04 2020 14:13:57
%S A170336 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T A170336 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U A170336 9304309958718547968,353563778431304822784,13435423580389583265792
%N A170336 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170336 The initial terms coincide with those of A170758, although the two sequences are eventually different.
%C A170336 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170336 <a href="/index/Rec#order_42">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, -703).
%F A170336 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170336 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170336 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170336 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170336 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 +
%F A170336 2*t + 1)/(703*t^42 - 37*t^41 - 37*t^40 - 37*t^39 - 37*t^38 - 37*t^37 -
%F A170336 37*t^36 - 37*t^35 - 37*t^34 - 37*t^33 - 37*t^32 - 37*t^31 - 37*t^30 -
%F A170336 37*t^29 - 37*t^28 - 37*t^27 - 37*t^26 - 37*t^25 - 37*t^24 - 37*t^23 -
%F A170336 37*t^22 - 37*t^21 - 37*t^20 - 37*t^19 - 37*t^18 - 37*t^17 - 37*t^16 -
%F A170336 37*t^15 - 37*t^14 - 37*t^13 - 37*t^12 - 37*t^11 - 37*t^10 - 37*t^9 -
%F A170336 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 A170336 coxG[{42,703,-37}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 04 2020 *)
%K A170336 nonn
%O A170336 0,2
%A A170336 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009