cp's OEIS Frontend

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.

A164025 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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%I A164025 #17 Sep 08 2022 08:45:47
%S A164025 1,28,756,20412,551124,14880348,401769018,10847753280,292889063376,
%T A164025 7907997281184,213515725982832,5764919185089792,155652671753506746,
%U A164025 4202618188762620900,113470584484975272828,3063702902583418604964
%N A164025 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
%C A164025 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A164025 Computed with MAGMA using commands similar to those used to compute A154638.
%H A164025 G. C. Greubel, <a href="/A164025/b164025.txt">Table of n, a(n) for n = 0..695</a>
%H A164025 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (26,26,26,26,26,-351).
%F A164025 G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%F A164025 a(n) = -351*a(n-6) + 26*Sum_{k=1..5} a(n-k). - _Wesley Ivan Hurt_, May 11 2021
%p A164025 seq(coeff(series((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), t, n+1), t, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A164025 CoefficientList[Series[(1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), {t,0,30}], t] (* _G. C. Greubel_, Sep 07 2017 *)
%t A164025 coxG[{6, 351, -26}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Aug 10 2019 *)
%o A164025 (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)) \\ _G. C. Greubel_, Sep 07 2017
%o A164025 (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7) )); // _G. C. Greubel_, Aug 13 2019
%o A164025 (Sage)
%o A164025 def A164025_list(prec):
%o A164025     P.<t> = PowerSeriesRing(ZZ, prec)
%o A164025     return P((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)).list()
%o A164025 A164025_list(30) # _G. C. Greubel_, Aug 13 2019
%o A164025 (GAP) a:=[28, 756, 20412, 551124, 14880348, 401769018];; for n in [7..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -351*a[n-6]; od; Concatenation([1], a); # _G. C. Greubel_, Aug 13 2019
%K A164025 nonn
%O A164025 0,2
%A A164025 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009