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%I #14 Sep 08 2022 08:45:48
%S 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543851,
%T 423262980,2539577145,15237458460,91424724300,548548187040,
%U 3291288169680,19747723302720,118486305524160,710917627392000,4265504529834660
%N Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A003949, 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="/A165782/b165782.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,5,5,5,5,5,5,5,-15).
%F G.f.: (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)/(15*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Sep 22 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), {t, 0, 30}], t] (* _G. C. Greubel_, Apr 08 2016 *)
%t coxG[{10, 15, -5}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 22 2019 *)
%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11)) \\ _G. C. Greubel_, Aug 07 2017
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) )); // _G. C. Greubel_, Sep 22 2019
%o (Sage)
%o def A165782_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) ).list()
%o A165782_list(30) # _G. C. Greubel_, Sep 22 2019
%o (GAP) a:=[7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851];; for n in [11..30] do a[n]:=5*Sum([1..9], j-> a[n-j]) -15*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 22 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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