A169062 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = 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 24: a(24) = 22842547657127204259279227556321042627432, A170768(24) = 22842547657127204259279227556321042628608. - Klaus Brockhaus, Apr 20 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, 47, 47, 47, -1128).

Formula

G.f.: (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)/(1128*t^24 - 47*t^23 - 47*t^22 - 47*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[{24, 1128, -47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 15 2024 *)

Crossrefs

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

Sequence in context: A168918 A168966 A169014 * A169110 A169158 A169206

Adjacent sequences: A169059 A169060 A169061 * A169063 A169064 A169065

Keyword

nonn

Author

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

Status

approved