A169384 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset

0,2

Comments

The initial terms coincide with those of A170754, although the two sequences are eventually different.

First disagreement at index 31: a(31) = 307918339166124058918933387670363175437635419565, A170754(31) = 307918339166124058918933387670363175437635420160. - 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 (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

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)/(561*t^31 - 33*t^30 - 33*t^29 - 33*t^28 - 33*t^27 - 33*t^26 - 33*t^25 - 33*t^24 - 33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 - 33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

Mathematica

coxG[{31, 561, -33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 07 2018 *)

Crossrefs

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

Sequence in context: A169240 A169288 A169336 * A169432 A169480 A169528

Adjacent sequences: A169381 A169382 A169383 * A169385 A169386 A169387

Keyword

nonn

Author

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

Status

approved