The On-Line Encyclopedia of Integer Sequences (OEIS)

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A163526

Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
(history; published version)

#18 by Charles R Greathouse IV at Thu Sep 08 08:45:46 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // G. C. Greubel, May 16 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#17 by Wesley Ivan Hurt at Mon May 10 13:04:38 EDT 2021

STATUS

editing

approved

#16 by Wesley Ivan Hurt at Mon May 10 13:04:32 EDT 2021

FORMULA

a(n) = 24*a(n-1)+24*a(n-2)+24*a(n-3)+24*a(n-4)-300*a(n-5). - Wesley Ivan Hurt, May 10 2021

STATUS

approved

editing

#15 by Bruno Berselli at Thu May 16 03:31:34 EDT 2019

STATUS

reviewed

approved

#14 by Michel Marcus at Thu May 16 02:24:28 EDT 2019

STATUS

proposed

reviewed

#13 by G. C. Greubel at Thu May 16 02:21:12 EDT 2019

STATUS

editing

proposed

#12 by G. C. Greubel at Thu May 16 02:20:48 EDT 2019

MATHEMATICA

CoefficientList[Series[(t1+x)*(1-x^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + )/(1)/(-25*x+324*x^5-300*t^5 - 24*t^4 - 24*t^3 - 24*tx^2 - 24*t + 16), {t, x, 0, 5020}], tx] (* G. C. Greubel, Jul 27 2017 *)

coxG[{5, 300, -24}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

PROG

(PARI) tmy(x='tx+O('tx^5020)); Vec((t1+x)*(1-x^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + )/(1)/(-25*x+324*x^5-300*t^5 - 24*t^4 - 24*t^3 - 24*tx^2 - 24*t + 16)) \\ G. C. Greubel, Jul 27 2017

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // G. C. Greubel, May 16 2019

(Sage) ((1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

STATUS

approved

editing

#11 by Bruno Berselli at Fri Jul 28 09:57:38 EDT 2017

STATUS

proposed

approved

#10 by Michel Marcus at Fri Jul 28 01:23:26 EDT 2017

STATUS

editing

proposed

#9 by Michel Marcus at Fri Jul 28 01:23:22 EDT 2017

FORMULA

G.f. : (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

STATUS

proposed

editing