A168901 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset

0,2

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 21497296922210633025156563250736, A170751(21) = 21497296922210633025156563251232. - Klaus Brockhaus, Apr 05 2011

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

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

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)/(465*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

Mathematica

With[{num=Total[2t^Range[20]]+t^21+1, den=Total[-30 t^Range[20]]+ 465t^21+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jul 18 2011 *)

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Sequence in context: A168757 A168805 A168853 * A168949 A168997 A169045

Adjacent sequences: A168898 A168899 A168900 * A168902 A168903 A168904

Keyword

nonn

Author

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

Status

approved