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A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

%I A164548 #12 Jul 18 2021 01:48:11
%S A164548 1,10,90,810,7290,65610,590490,5314365,47828880,430456320,3874074480,
%T A164548 34866378720,313794784080,2824129437120,25416952359660,
%U A164548 228750658083360,2058738704511840,18528493377756960,166755045745830240
%N A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164548 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A164548 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164548 G. C. Greubel, <a href="/A164548/b164548.txt">Table of n, a(n) for n = 0..1000</a>
%H A164548 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,8,8,8,8,8,-36).
%F A164548 G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
%F A164548 G.f.: (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8). - _G. C. Greubel_, Jul 17 2021
%t A164548 CoefficientList[Series[(1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8), {t,0,30}], t] (* or *)
%t A164548 coxG[{7, 36, -8, 30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Jul 17 2021 *)
%o A164548 (Magma)
%o A164548 R<t>:=PowerSeriesRing(Integers(), 30);
%o A164548 Coefficients(R!( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) )); // _G. C. Greubel_, Jul 17 2021
%o A164548 (Sage)
%o A164548 def A168823_list(prec):
%o A164548     P.<t> = PowerSeriesRing(ZZ, prec)
%o A164548     return P( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) ).list()
%o A164548 A168823_list(30) # _G. C. Greubel_, Jul 17 2021
%K A164548 nonn
%O A164548 0,2
%A A164548 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009