A166420 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222655925, 61988830566390000, 1549720764159547200, 38743019103983610000, 968575477599463500000

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 (24,24,24,24,24,24,24,24,24,24,-300).

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)/(300*t^11 - 24*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).

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

a(n) = 24*Sum_{j=1..10} a(n-j) - 300*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 25*x + 324*x^11 - 300*x^12). (End)

Mathematica

With[{p=300, q=24}, 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, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 31 2017 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-25*x+324*x^11-300*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166420_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-25*x+324*x^11-300*x^12) ).list()
A166420_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170745.

Sequence in context: A164964 A165369 A165973 * A166613 A167079 A167225

Adjacent sequences: A166417 A166418 A166419 * A166421 A166422 A166423

Keyword

nonn

Author

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

Status

approved