A166165 - OEIS

%I #12 Mar 11 2020 17:11:45

%S 1,36,1260,44100,1543500,54022500,1890787500,66177562500,

%T 2316214687500,81067514062500,2837362992186870,99307704726518400,

%U 3475769665427372880,121651938289931061600,4257817840146642534000,149023624405099426920000

%N Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

%C The initial terms coincide with those of A170755, 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="/A166165/b166165.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 (34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

%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)/(595*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

%p seq(coeff(series((1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Mar 11 2020

%t CoefficientList[Series[(1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11), {t,0,30}], t] (* _G. C. Greubel_, May 06 2016 *)

%t coxG[{595, 10, -34}] (* The coxG program is in A169452 *) (* _G. C. Greubel_, Mar 11 2020 *)

%o (Sage)

%o def A166165_list(prec):

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

%o     return P( (1+t)*(1-t^10)/(1-35*t+629*t^10-595*t^11) ).list()

%o A166165_list(30) # _G. C. Greubel_, Mar 11 2020

%K nonn

%O 0,2

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