A169124 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360

Offset

0,2

Comments

The initial terms coincide with those of A170734, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 674981937087725596717728399255, A170734(26) = 674981937087725596717728399360. - Klaus Brockhaus, Apr 30 2011

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

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).

Formula

G.f.: (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)/(91*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

Mathematica

coxG[{26, 91, -13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 08 2018 *)

Crossrefs

Cf. A170734 (G.f.: (1+x)/(1-14*x)).

Sequence in context: A168980 A169028 A169076 * A169172 A169220 A169268

Adjacent sequences: A169121 A169122 A169123 * A169125 A169126 A169127

Keyword

nonn

Author

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

Status

approved