A169234 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176

Offset

0,2

Comments

The initial terms coincide with those of A170748, although the two sequences are eventually different.

First disagreement at index 28: a(28) = 34329291795869566821950325690984770305642, A170748(28) = 34329291795869566821950325690984770306048. - Klaus Brockhaus, May 24 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 (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

Formula

G.f.: (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)/(378*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

Mathematica

coxG[{28, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 03 2023 *)

Crossrefs

Cf. A170748 (G.f.: (1+x)/(1-28*x)).

Sequence in context: A169090 A169138 A169186 * A169282 A169330 A169378

Adjacent sequences: A169231 A169232 A169233 * A169235 A169236 A169237

Keyword

nonn

Author

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

Status

approved