A169155 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750, 6422927569141882324218750, 289031740611384704589843750

Offset

0,2

Comments

The initial terms coincide with those of A170765, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 9841712544508343661854104399681091308592715, A170765(26) = 9841712544508343661854104399681091308593750. - 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 (44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,-990).

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)/(990*t^26 - 44*t^25 - 44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 - 44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).

Mathematica

With[{num=Total[2t^Range[25]]+t^26+1, den=Total[-44 t^Range[25]]+ 990t^26+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 24 2013 *)

Crossrefs

Cf. A154638, A170765 (g.f.: (1+x)/(1-45*x)).

Sequence in context: A170631 A170679 A170727 * A170151 A170765 A218748

Adjacent sequences: A169152 A169153 A169154 * A169156 A169157 A169158

Keyword

nonn,easy

Author

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

Extensions

a(15)-a(16) from Pontus von Brömssen, May 05 2026

Status

approved