A164030 - OEIS

%I #19 Sep 08 2022 08:45:47

%S 1,31,930,27900,837000,25110000,753299535,22598972100,677968744965,

%T 20339049807900,610171118005500,18305122253220000,549153328988465760,

%U 16474589711416216125,494237386595541683490,14827112455463543698875

%N Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

%C The initial terms coincide with those of A170750, 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="/A164030/b164030.txt">Table of n, a(n) for n = 0..675</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (29,29,29,29,29,-435).

%F G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

%F a(n) = -435*a(n-6) + 29*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021

%p seq(coeff(series((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019

%t coxG[{6,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 29 2016 *)

%t CoefficientList[Series[(1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 07 2017 *)

%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7)) \\ _G. C. Greubel_, Sep 07 2017

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7) )); // _G. C. Greubel_, Aug 13 2019

%o (Sage)

%o def A164030_list(prec):

%o     P.<t> = PowerSeriesRing(ZZ, prec)

%o     return P((1+t)*(1-t^6)/(1-30*t+464*t^6-435*t^7)).list()

%o A164030_list(30) # _G. C. Greubel_, Aug 13 2019

%o (GAP) a:=[31, 930, 27900, 837000, 25110000, 753299535];; for n in [7..30] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -435*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 13 2019

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009