A166601 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964190, 44266298381316000, 841059669244935600, 15980133715652476800

Offset

0,2

Comments

The initial terms coincide with those of A170739, 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 (18,18,18,18,18,18,18,18,18,18,18,-171).

Formula

G.f.: (t^12 + 2*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)/(171*t^12 - 18*t^11 - 18*t^10 - 18*t^9 -18*t^8 -18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -18*t + 1).

From G. C. Greubel, Dec 30 2024: (Start)

a(n) = 18*Sum_{j=1..11} a(n-j) - 171*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 19*x + 189*x^12 - 171*x^13). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^12)/(1-19*t+189*t^12-171*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 18 2016; Dec 30 2024 *)
coxG[{12, 171, -18}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 30 2024 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x)*(1-x^12)/(1-19*x+189*x^12-171*x^13) )); // G. C. Greubel, Dec 30 2024
(SageMath)
def A166601_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-19*x+189*x^12-171*x^13) ).list()
A166601_list(50) # G. C. Greubel, Dec 30 2024

Crossrefs

Cf. A154638, A169452, A170739.

Sequence in context: A165882 A063815 A166414 * A167073 A167148 A167680

Adjacent sequences: A166598 A166599 A166600 * A166602 A166603 A166604

Keyword

nonn

Author

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

Status

approved