A168881 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003954, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 8072999939190720110346, A003954(21) = 8072999939190720110412. - Klaus Brockhaus, Apr 05 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..950
• Index entries for linear recurrences with constant coefficients, signature (10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,-55).

Crossrefs

Cf. A003954 (G.f.: (1+x)/(1-11*x)).

Programs

Magma

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22) )); // G. C. Greubel, Sep 25 2019

Maple

seq(coeff(series((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 25 2019

Mathematica

CoefficientList[Series[(1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22), {t, 0, 20}], t] (* G. C. Greubel, Sep 25 2019 *)
coxG[{21, 55, -10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 25 2019 *)

PARI

my(t='t+O('t^20)); Vec((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22)) \\ G. C. Greubel, Sep 25 2019

Sage

def A168881_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^21)/(1-11*t+65*t^21-55*t^22)).list()
A168881_list(20) # G. C. Greubel, Sep 25 2019

Formula

G.f.: (t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/(55*t^21 - 10*t^20 - 10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).

G.f.: (1+t)*(1-t^21)/(1 -11*t +65*t^21 -55*t^22). - G. C. Greubel, Sep 25 2019