A166585 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162754936, 4785074604076800, 76561193665194120, 1224979098642551040, 19599665578271938560

Offset

0,2

Comments

The initial terms coincide with those of A170736, 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 (15,15,15,15,15,15,15,15,15,15,15,-120).

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)/(120*t^12 - 15*t^11 - 15*t^10 - 15*t^9 -15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 -15*t +1).

From G. C. Greubel, Dec 04 2024: (Start)

a(n) = 15*Sum_{j=1..11} a(n-j) - 120*a(n-12).

G.f.: (1+x)*(1-x^12)/(1 - 16*x + 135*x^12 - 120*x^13). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^12)/(1-16*t+135*t^12-120*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 17 2016; Dec 04 2024 *)
coxG[{16, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 04 2024 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^12)/(1-16*x+135*x^12-120*x^13) )); // G. C. Greubel, Dec 04 2024
(SageMath)
def A166585_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-16*x+135*x^12-120*x^13) ).list()
A166585_list(40) # G. C. Greubel, Dec 04 2024

Crossrefs

Cf. A154638, A169452, A170736.

Sequence in context: A165321 A165879 A166411 * A167027 A167124 A167673

Adjacent sequences: A166582 A166583 A166584 * A166586 A166587 A166588

Keyword

nonn

Author

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

Status

approved