A166412 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890207929, 616894133532192, 10487200270003200, 178282404589305312, 3030800878005455808, 51523614925876262304

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170737, 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 (16,16,16,16,16,16,16,16,16,16,-136).

Crossrefs

Cf. A154638, A169452, A170737.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-17*x+152*x^11-136*x^12) )); // G. C. Greubel, Jul 23 2024

Mathematica

CoefficientList[Series[(1+t)*(1-t^11)/(1-17*t+152*t^11-136*t^12), {t, 0,50}], t] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)
coxG[{11, 136, -16, 30}] (* The coxG program is at A169452 *)(* G. C. Greubel, Jul 23 2024 *)

SageMath

def A166412_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-17*x+152*x^11-136*x^12) ).list()
A166412_list(30) # G. C. Greubel, Jul 23 2024

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)/(136*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

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

a(n) = 16*Sum_{j=1..10} a(n-j) - 136*a(n-11).

G.f.: (1+x)*(1 - x^11)/(1 - 17*x + 152*x^11 - 136*x^12). (End)