A166421 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582640801, 99099301148651700, 2576581829864707275, 66991127576476229100, 1741769316988221795300

Offset

0,2

Comments

The initial terms coincide with those of A170746, 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 (25,25,25,25,25,25,25,25,25,25,-325).

Formula

G.f.: (t^11 + 2*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)/(325*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

From G. C. Greubel, Jan 17 2023: (Start)

a(n) = 25*Sum_{j=1..10} a(n-j) - 325*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 26*x + 350*x^11 - 325*x^12). (End)

Mathematica

With[{p=325, q=25}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t, 0, 40}], t]] (* G. C. Greubel, May 13 2016; Jul 25 2024 *)
coxG[{11, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 22 2021 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166421_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-26*x+350*x^11-325*x^12) ).list()
A166421_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170746.

Sequence in context: A164969 A165445 A165979 * A166614 A167080 A167226

Adjacent sequences: A166418 A166419 A166420 * A166422 A166423 A166424

Keyword

nonn

Author

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

Status

approved