A166543 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596045, 2824295364000, 25418658272400, 228767924419200, 2058911319481200, 18530201872706400, 166771816830738000

Offset

0,2

Comments

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,8,8,-36).

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)/(36*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

From G. C. Greubel, Aug 23 2024: (Start)

a(n) = 8*Sum_{j=1..11} a(n-j) - 36*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 9*x + 44*x^12 - 36*x^13). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^12)/(1-9*t+44*t^12-36*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 16 2016; Aug 23 2024 *)
coxG[{12, 36, -8, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 23 2024 *)

Prog

(Magma)
R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-9*x+44*x^12-36*x^13) )); // G. C. Greubel, Aug 23 2024
(SageMath)
def A166543_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-9*x+44*x^12-36*x^13) ).list()
A166543_list(30) # G. C. Greubel, Aug 23 2024

Crossrefs

Cf. A003952, A154638, A169452.

Sequence in context: A165219 A165788 A166368 * A166933 A167111 A167659

Adjacent sequences: A166540 A166541 A166542 * A166544 A166545 A166546

Keyword

nonn

Author

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

Status

approved