A169378 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = 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 31: a(31) = 753596613502928730875453549568497677758365290, A170748(31) = 753596613502928730875453549568497677758365696. - 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 (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, 27, 27, 27, -378).

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)/(378*t^31 - 27*t^30 - 27*t^29 - 27*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[{31, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 17 2023 *)

Crossrefs

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

Sequence in context: A169234 A169282 A169330 * A169426 A169474 A169522

Adjacent sequences: A169375 A169376 A169377 * A169379 A169380 A169381

Keyword

nonn

Author

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

Status

approved