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A164331 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164331 #17 Sep 08 2022 08:45:47
%S A164331 1,46,2070,93150,4191750,188628750,8488292715,381973125600,
%T A164331 17188788557160,773495390804400,34807288344147000,1566327784594320000,
%U A164331 70484741716592195190,3171812990689846701000,142731567185989127785560
%N A164331 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164331 The initial terms coincide with those of A170765, although the two sequences are eventually different.
%C A164331 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164331 G. C. Greubel, <a href="/A164331/b164331.txt">Table of n, a(n) for n = 0..600</a>
%H A164331 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (44,44,44,44,44,-990).
%F A164331 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
%F A164331 a(n) = -990*a(n-6) + 44*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164331 seq(coeff(series((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 16 2019
%t A164331 CoefficientList[Series[(1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 14 2017 *)
%t A164331 coxG[{6, 990, -44}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 16 2019 *)
%o A164331 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7)) \\ _G. C. Greubel_, Sep 14 2017
%o A164331 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7) )); // _G. C. Greubel_, Aug 16 2019
%o A164331 (Sage)
%o A164331 def A164331_list(prec):
%o A164331     P.<t> = PowerSeriesRing(ZZ, prec)
%o A164331     return P((1+t)*(1-t^6)/(1-45*t+1034*t^6-990*t^7)).list()
%o A164331 A164331_list(30) # _G. C. Greubel_, Aug 16 2019
%o A164331 (GAP) a:=[46, 2070, 93150, 4191750, 188628750, 8488292715];; for n in [7..30] do a[n]:=44*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -990*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 16 2019
%K A164331 nonn
%O A164331 0,2
%A A164331 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009