A164601 - OEIS

%I #17 Sep 08 2022 08:45:47

%S 1,12,132,1452,15972,175692,1932612,21258666,233844600,2572282680,

%T 28295022360,311244287640,3423676622520,37660326891000,

%U 414262320281370,4556871492422700,50125432079728500,551378055176107500

%N Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

%C The initial terms coincide with those of A003954, 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="/A164601/b164601.txt">Table of n, a(n) for n = 0..950</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,10,10,10,10,10,-55).

%F G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(55*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

%F a(n) = -55*a(n-7) + 10*Sum_{k=1..6} a(n-k). - _Wesley Ivan Hurt_, May 11 2021

%p seq(coeff(series((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 28 2019

%t CoefficientList[Series[(1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8), {t, 0, 30}], t] (* _G. C. Greubel_, Aug 11 2017 *)

%t coxG[{7, 55, -10}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 28 2019 *)

%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)) \\ _G. C. Greubel_, Aug 11 2017

%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8) )); // _G. C. Greubel_, Aug 28 2019

%o (Sage)

%o def A164601_list(prec):

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

%o     return P((1+t)*(1-t^7)/(1-11*t+65*t^7-55*t^8)).list()

%o A164601_list(30) # _G. C. Greubel_, Aug 28 2019

%o (GAP) a:=[12, 132, 1452, 15972, 175692, 1932612, 21258666];; for n in [8..30] do a[n]:=10*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -55*a[n-7]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 28 2019

%K nonn

%O 0,2

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