A169371 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset

0,2

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.

First disagreement at index 31: a(31) = 102094306360577610211441129338452806400991, A170741(31) = 102094306360577610211441129338452806401222. - Klaus Brockhaus, Jun 17 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Formula

G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*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)/(210*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

Mathematica

With[{num=Total[2t^Range[30]]+t^31+1, den=Total[-20 t^Range[30]]+ 210t^31+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Sep 21 2011 *)

Crossrefs

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

Sequence in context: A169227 A169275 A169323 * A169419 A169467 A169515

Adjacent sequences: A169368 A169369 A169370 * A169372 A169373 A169374

Keyword

nonn

Author

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

Status

approved