A166430 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726561870, 3475769665429643400, 121651938290036747880, 4257817840151259186600, 149023624405293126909000

Offset

0,2

Comments

The initial terms coincide with those of A170755, 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 (34,34,34,34,34,34,34,34,34,34,-595).

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)/(595*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

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

a(n) = 34*Sum_{j=1..10} a(n-j) - 595*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 35*x + 629*x^11 - 595*x^12). (End)

Mathematica

With[{p=595, q=34}, 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 *)
coxG[{11, 595, -34, 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)/(1-35*x+629*x^11-595*x^12) )); // G. C. Greubel, Jul 25 2024
(SageMath)
def A166430_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-35*x+629*x^11-595*x^12) ).list()
A166430_list(30) # G. C. Greubel, Jul 25 2024

Crossrefs

Cf. A154638, A169452, A170755.

Sequence in context: A165168 A165651 A166165 * A166688 A167089 A167429

Adjacent sequences: A166427 A166428 A166429 * A166431 A166432 A166433

Keyword

nonn

Author

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

Status

approved