A166426 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385136, 813071260684923840, 25205209081232162880, 781361481518182288320, 24222205927063193348160

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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 (30,30,30,30,30,30,30,30,30,30,-465).

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)/(465*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

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

a(n) = 30*Sum_{j=1..10} a(n-j) - 465*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 31*x + 495*x^11 - 465*x^12). (End)

Mathematica

coxG[{11, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 06 2015 *)
With[{p=465, q=30}, 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 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-31*x+495*x^11-465*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166426_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-31*x+495*x^11-465*x^12) ).list()
A166426_list(30) # G. C. Greubel, Jul 25 2024
(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)*(1+x)/(1-30*x-30*x^2-30*x^3-30*x^4-30*x^5-30*x^6-30*x^7-30*x^8-30*x^9-30*x^10+465*x^11)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A154638, A169452, A170751.

Sequence in context: A165131 A165548 A166128 * A166622 A167085 A167382

Adjacent sequences: A166423 A166424 A166425 * A166427 A166428 A166429

Keyword

nonn,easy

Author

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

Status

approved