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%I #12 Nov 24 2016 10:32:18
%S 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U 25205209081233591856,781361481518241332160,24222205927065480820800
%N Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
%C The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C Computed with MAGMA using commands similar to those used to compute A154638.
%H G. C. Greubel, <a href="/A167085/b167085.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F G.f.: (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)/(465*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%t CoefficientList[Series[(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)/(465*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 01 2016 *)
%t coxG[{13,465,-30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 24 2016 *)
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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