A168918 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192

Offset

0,2

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 206547920800123013050484913522867048, A170768(21) = 206547920800123013050484913522868224. - Klaus Brockhaus, Apr 08 2011

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

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).

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)/(1128*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

Mathematica

coxG[{21, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 23 2019 *)

Crossrefs

Cf. A170768 (G.f.: (1+x)/(1-48*x)).

Sequence in context: A168774 A168822 A168870 * A168966 A169014 A169062

Adjacent sequences: A168915 A168916 A168917 * A168919 A168920 A168921

Keyword

nonn

Author

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

Status

approved