A166423 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234166890, 240511774556661552, 6734329687586205558, 188561231252404854480, 5279714475067086693408

Offset

0,2

Comments

The initial terms coincide with those of A170748, 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 (27,27,27,27,27,27,27,27,27,27,-378).

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)/(378*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

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

a(n) = 27*Sum_{j=1..10} a(n-j) - 378*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 28*x + 405*x^11 - 378*x^12). (End)

Mathematica

With[{p=378, q=27}, 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, 378, -27, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 25 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-28*x+405*x^11-378*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166423_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-28*x+405*x^11-378*x^12) ).list()
A166423_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170748.

Sequence in context: A164974 A165512 A166004 * A166616 A167082 A167285

Adjacent sequences: A166420 A166421 A166422 * A166424 A166425 A166426

Keyword

nonn

Author

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

Status

approved