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%I #17 Sep 08 2022 08:45:47
%S 1,48,2256,106032,4983504,234224688,11008559208,517402229760,
%T 24317902308096,1142941291421184,53718235195007232,
%U 2524756795581284352,118663557238871024856,5577186619014877732560,262127744246735162576688
%N Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C The initial terms coincide with those of A170767, 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="/A164348/b164348.txt">Table of n, a(n) for n = 0..595</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, -1081).
%F G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%F a(n) = -1081*a(n-6) + 46*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 07 2021
%p seq(coeff(series((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), t, n+1), t, n), n = 0..20); # _G. C. Greubel_, Aug 24 2019
%t CoefficientList[Series[(1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), {t, 0, 20}], t] (* _G. C. Greubel_, Sep 15 2017 *)
%t coxG[{6, 1081, -46}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 24 2019 *)
%o (PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)) \\ _G. C. Greubel_, Sep 15 2017
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7) )); // _G. C. Greubel_, Aug 24 2019
%o (Sage)
%o def A164348_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)).list()
%o A164348_list(20) # _G. C. Greubel_, Aug 24 2019
%o (GAP) a:=[48, 2256, 106032, 4983504, 234224688, 11008559208];; for n in [7..20] do a[n]:=46*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1081*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 24 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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