A166434 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407663260, 12699033492898836720, 495262306223053446480, 19315229942699038174320

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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 (38,38,38,38,38,38,38,38,38,38,-741).

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)/(741*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

From G. C. Greubel, Jul 25 2024: (Start)

a(n) = 38*Sum_{j=1..10} a(n-j) - 741*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 39*x + 779*x^11 - 741*x^12). (End)

Mathematica

coxG[{11, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 10 2015 *)
With[{p=741, q=38}, 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 14 2016; Jul 25 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-39*x+779*x^11-741*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166434_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-39*x+779*x^11-741*x^12) ).list()
A166434_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170759.

Sequence in context: A165172 A165690 A166172 * A166693 A167093 A167538

Adjacent sequences: A166431 A166432 A166433 * A166435 A166436 A166437

Keyword

nonn

Author

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

Status

approved