A168949 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = 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.

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

From Klaus Brockhaus, Apr 10 2011: (Start)

First disagreement between this sequence and A170751 is at index 22:

a(22) = 666416204588529623779853460787696,

A170751(22) = 666416204588529623779853460788192. (End)

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, 30, -465).

Formula

G.f.: (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)/(465*t^22 - 30*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[21]]+t^22+1, den=Total[-30 t^Range[21]]+ 465t^22+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 06 2013 *)

Crossrefs

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

Sequence in context: A168805 A168853 A168901 * A168997 A169045 A169093

Adjacent sequences: A168946 A168947 A168948 * A168950 A168951 A168952

Keyword

nonn

Author

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

Extensions

Edited by Jon E. Schoenfield, Apr 30 2014

Status

approved