A166429 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392091565, 2456609527331092980, 83524723929256474095, 2839840613594696753580, 96554580862218895189620

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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 (33,33,33,33,33,33,33,33,33,33,-561).

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)/(561*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

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

a(n) = 33*Sum_{j=1..10} a(n-j) - 561*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 34*x + 594*x^11 - 561*x^12). (End)

Mathematica

With[{p=561, q=33}, 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, 561, -33, 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)/(1-34*x+594*x^11-561*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166429_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-34*x+594*x^11-561*x^12) ).list()
A166429_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170754.

Sequence in context: A165167 A165650 A166145 * A166683 A167088 A167405

Adjacent sequences: A166426 A166427 A166428 * A166430 A166431 A166432

Keyword

nonn

Author

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

Status

approved