|
%I #15 Sep 08 2022 08:45:48
%S 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T 1879463646744,43227663874836,994236269114880,22867434189496512,
%U 525950986355068032,12096872686089474624,278228071778284843776
%N Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
%C The initial terms coincide with those of A170743, 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="/A165965/b165965.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 (22,22,22,22,22,22,22,22,22,-253).
%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)/(253*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
%p seq(coeff(series((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), t, n+1), t, n), n = 0..30); # _G. C. Greubel_, Sep 26 2019
%t CoefficientList[Series[(1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11), {t, 0, 25}], t] (* _G. C. Greubel_, Apr 18 2016 *)
%t coxG[{10, 253, -22}] (* The coxG program is at A169452 *) (* _G. C. Greubel_, Sep 26 2019 *)
%o (PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)) \\ _G. C. Greubel_, Sep 26 2019
%o (Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11) )); // _G. C. Greubel_, Sep 26 2019
%o (Sage)
%o def A165965_list(prec):
%o P.<t> = PowerSeriesRing(ZZ, prec)
%o return P((1+t)*(1-t^10)/(1-23*t+275*t^10-253*t^11)).list()
%o A165965_list(30) # _G. C. Greubel_, Sep 26 2019
%o (GAP) a:=[24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663874836];; for n in [11..30] do a[n]:=22*Sum([1..9], j-> a[n-j]) -253*a[n-10]; od; Concatenation([1], a); # _G. C. Greubel_, Sep 26 2019
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
|
