This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164373 #16 Sep 08 2022 08:45:47
%S A164373 1,8,56,392,2744,19208,134456,941164,6587952,46114320,322790832,
%T A164373 2259469968,15815828784,110707574544,774930433956,5424354927432,
%U A164373 37969377752376,265777897314888,1860391054122552,13022357800350024
%N A164373 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
%C A164373 The initial terms coincide with those of A003950, although the two sequences are eventually different.
%C A164373 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164373 G. C. Greubel, <a href="/A164373/b164373.txt">Table of n, a(n) for n = 0..1000</a>
%H A164373 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6, 6, 6, 6, 6, 6, -21).
%F A164373 G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).
%F A164373 a(n) = -21*a(n-7) + 6*Sum_{k=1..6} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164373 seq(coeff(series((1+t)*(1-t^7)/(1-7*t+27*t^7-21*t^8), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 28 2019
%t A164373 CoefficientList[Series[(1+t)*(1-t^7)/(1-7*t+27*t^7-21*t^8), {t, 0, 30}], t] (* _G. C. Greubel_, Sep 17 2017 *)
%t A164373 coxG[{7, 21, -6}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 28 2019 *)
%o A164373 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-7*t+27*t^7-21*t^8)) \\ _G. C. Greubel_, Sep 17 2017
%o A164373 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-7*t+27*t^7-21*t^8) )); // _G. C. Greubel_, Aug 28 2019
%o A164373 (Sage)
%o A164373 def A164373_list(prec):
%o A164373 P.<t> = PowerSeriesRing(ZZ, prec)
%o A164373 return P((1+t)*(1-t^7)/(1-7*t+27*t^7-21*t^8)).list()
%o A164373 A164373_list(30) # _G. C. Greubel_, Aug 28 2019
%o A164373 (GAP) a:=[8, 56, 392, 2744, 19208, 134456, 941164];; for n in [8..30] do a[n]:=6*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -21*a[n-7]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 28 2019
%K A164373 nonn
%O A164373 0,2
%A A164373 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009