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A164277 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%I A164277 #17 Sep 08 2022 08:45:47
%S A164277 1,44,1892,81356,3498308,150427244,6468370546,278139892800,
%T A164277 11960013642192,514280511441312,22114058759539824,950904387665438976,
%U A164277 40888882692839511330,1758221698790838894228,75603521996953503778764
%N A164277 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164277 The initial terms coincide with those of A170763, although the two sequences are eventually different.
%C A164277 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164277 G. C. Greubel, <a href="/A164277/b164277.txt">Table of n, a(n) for n = 0..610</a>
%H A164277 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (42,42,42,42,42,-903).
%F A164277 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
%F A164277 a(n) = -903*a(n-6) + 42*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164277 seq(coeff(series((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 16 2019
%t A164277 CoefficientList[Series[(1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 12 2017 *)
%t A164277 coxG[{6, 903, -42}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 16 2019 *)
%o A164277 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7)) \\ _G. C. Greubel_, Sep 12 2017
%o A164277 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7) )); // _G. C. Greubel_, Aug 16 2019
%o A164277 (Sage)
%o A164277 def A164277_list(prec):
%o A164277     P.<t> = PowerSeriesRing(ZZ, prec)
%o A164277     return P((1+t)*(1-t^6)/(1-43*t+945*t^6-903*t^7)).list()
%o A164277 A164277_list(30) # _G. C. Greubel_, Aug 16 2019
%o A164277 (GAP) a:=[44, 1892, 81356, 3498308, 150427244, 6468370546];; for n in [7..30] do a[n]:=42*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -903*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 16 2019
%K A164277 nonn
%O A164277 0,2
%A A164277 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009