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 A164050 #22 Jun 10 2025 23:15:35
%S A164050 1,34,1122,37026,1221858,40321314,1330602801,43909873920,
%T A164050 1449025228992,47817812414592,1577987144990784,52073553849901056,
%U A164050 1718426553198820080,56708052368589946368,1871364939893753424384,61755017003604231740928
%N A164050 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164050 The initial terms coincide with those of A170753, although the two sequences are eventually different.
%C A164050 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164050 G. C. Greubel, <a href="/A164050/b164050.txt">Table of n, a(n) for n = 0..655</a>
%H A164050 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (32,32,32,32,32,-528).
%F A164050 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
%F A164050 a(n) = -528*a(n-6) + 32*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164050 seq(coeff(series((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A164050 CoefficientList[Series[(1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 08 2017 *)
%t A164050 LinearRecurrence[{32,32,32,32,32, -528}, {1,34,1122,37026, 1221858, 40321314, 1330602801}, 21] (* _Vincenzo Librandi_, Sep 09 2017 *)
%t A164050 coxG[{6, 528, -2}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 13 2019 *)
%o A164050 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)) \\ _G. C. Greubel_, Sep 08 2017
%o A164050 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7) )); // _G. C. Greubel_, Aug 13 2019
%o A164050 (Sage)
%o A164050 def A164050_list(prec):
%o A164050 P.<t> = PowerSeriesRing(ZZ, prec)
%o A164050 return P((1+t)*(1-t^6)/(1-33*t+560*t^6-528*t^7)).list()
%o A164050 A164050_list(30) # _G. C. Greubel_, Aug 13 2019
%o A164050 (GAP) a:=[34, 1122, 37026, 1221858, 40321314, 1330602801];; for n in [7..30] do a[n]:=32*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -528*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 13 2019
%K A164050 nonn
%O A164050 0,2
%A A164050 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009