A165973 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128905925, 2479553222640000, 61988830565797200, 1549720764139860000, 38743019103369750000, 968575477581075000000

Offset

0,2

Comments

The initial terms coincide with those of A170745, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (24,24,24,24,24,24,24,24,24,-300).

Formula

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)/(300*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

Maple

seq(coeff(series((1+t)*(1-t^10)/(1-25*t+324*t^10-300*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019

Mathematica

coxG[{10, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 03 2016 *)
CoefficientList[Series[(1+t)*(1-t^10)/(1-25*t+324*t^10-300*t^11), {t, 0, 25}], t] (* G. C. Greubel, Sep 26 2019 *)

Prog

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-25*t+324*t^10-300*t^11)) \\ G. C. Greubel, Sep 26 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-25*t+324*t^10-300*t^11) )); // G. C. Greubel, Sep 26 2019
(Sage)
def A165973_list(prec):
    P.<t> = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-25*t+324*t^10-300*t^11)).list()
A165973_list(30) # G. C. Greubel, Sep 26 2019
(GAP) a:=[26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128905925];; for n in [11..30] do a[n]:=24*Sum([1..9], j-> a[n-j]) -300*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019

Crossrefs

Sequence in context: A164639 A164964 A165369 * A166420 A166613 A167079

Adjacent sequences: A165970 A165971 A165972 * A165974 A165975 A165976

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved