A166432 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151877559, 6760869627619443672, 250152176221918454160, 9255630520210947220872

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170757, 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 (36,36,36,36,36,36,36,36,36,36,-666).

Crossrefs

Cf. A154638, A169452, A170757.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-37*x+702*x^11-666*x^12) )); // G. C. Greubel, Jul 25 2024

Mathematica

With[{p=666, q=36}, 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[{11,666,-36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 26 2016 *)

SageMath

def A166432_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-37*x+702*x^11-666*x^12) ).list()
A166432_list(30) # G. C. Greubel, Jul 25 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)/(666*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

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

a(n) = 26*Sum_{j=1..10} a(n-j) - 351*a(n-11).

G.f.: (1+x)*(1-x^11)/(1 - 37*x + 702*x^11 - 666*x^12). (End)