A169025 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

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

Offset

0,2

Comments

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

First disagreement at index 24: a(24) = 10745162919062848466958306, A003954(24) = 10745162919062848466958372. - Klaus Brockhaus, Apr 20 2011

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

Links

Table of n, a(n) for n=0..17.

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, 10, 10, 10, -55).

Formula

G.f.: (t^24 + 2*t^23 + 2*t^22 + 2*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^24 - 10*t^23 - 10*t^22 - 10*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).

Mathematica

With[{num=Total[2t^Range[23]]+t^24+1, den=Total[-10 t^Range[23]]+ 55t^24+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Sep 18 2011 *)

Crossrefs

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

Sequence in context: A168881 A168929 A168977 * A169073 A169121 A169169

Adjacent sequences: A169022 A169023 A169024 * A169026 A169027 A169028

Keyword

nonn

Author

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

Status

approved