A169121 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = 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 26: a(26) = 1300164713206604664501962946, A003954(26) = 1300164713206604664501963012. - Klaus Brockhaus, Apr 30 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, 10, 10, -55).

Formula

G.f.: (t^26 + 2*t^25 + 2*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^26 - 10*t^25 - 10*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[25]]+t^26+1, den=Total[-10 t^Range[25]]+55t^26+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, May 10 2012 *)

Crossrefs

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

Sequence in context: A168977 A169025 A169073 * A169169 A169217 A169265

Adjacent sequences: A169118 A169119 A169120 * A169122 A169123 A169124

Keyword

nonn

Author

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

Status

approved