A168854 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992

Offset

0,2

Comments

The initial terms coincide with those of A170752, although the two sequences are eventually different.

First disagreement at index 20: a(20) = 1307264681485361570293475180016, A170752(20) = 1307264681485361570293475180544. - Klaus Brockhaus, Apr 04 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 (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).

Formula

G.f.: (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)/(496*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).

Mathematica

With[{num=Total[2t^Range[19]]+t^20+1, den=Total[-31 t^Range[19]]+ 496t^20+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 11 2011 *)

Crossrefs

Cf. A170752 (G.f.: (1+x)/(1-32*x)).

Sequence in context: A168710 A168758 A168806 * A168902 A168950 A168998

Adjacent sequences: A168851 A168852 A168853 * A168855 A168856 A168857

Keyword

nonn

Author

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

Status

approved