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A164036 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164036 #16 Sep 08 2022 08:45:47
%S A164036 1,32,992,30752,953312,29552672,916132336,28400087040,880402222080,
%T A164036 27292454123520,846065620239360,26228020042137600,813068181562751760,
%U A164036 25205099996403756000,781357677295456980000,24222074895781408504800,750883915657732812602400
%N A164036 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164036 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A164036 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164036 G. C. Greubel, <a href="/A164036/b164036.txt">Table of n, a(n) for n = 0..665</a>
%H A164036 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (30,30,30,30,30,-465).
%F A164036 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%F A164036 a(n) = -465*a(n-6) + 30*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164036 seq(coeff(series((1+t)*(1-t^6)/(1-31*t+495*t^6-465*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A164036 CoefficientList[Series[(1+t)*(1-t^6)/(1-31*t+495*t^6-465*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 08 2017 *)
%t A164036 coxG[{6, 465, -30}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 13 2019 *)
%o A164036 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-31*t+495*t^6-465*t^7)) \\ _G. C. Greubel_, Sep 08 2017
%o A164036 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-31*t+495*t^6-465*t^7) )); // _G. C. Greubel_, Aug 13 2019
%o A164036 (Sage)
%o A164036 def A164036_list(prec):
%o A164036     P.<t> = PowerSeriesRing(ZZ, prec)
%o A164036     return P((1+t)*(1-t^6)/(1-31*t+495*t^6-465*t^7)).list()
%o A164036 A164036_list(30) # _G. C. Greubel_, Aug 13 2019
%o A164036 (GAP) a:=[32, 992, 30752, 953312, 29552672, 916132336];; for n in [7..30] do a[n]:=30*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -465*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 13 2019
%K A164036 nonn
%O A164036 0,2
%A A164036 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009