A168885 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000

Offset

0,2

Comments

The initial terms coincide with those of A170735, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 5320410768127441406249880, A170735(21) = 5320410768127441406250000. - Klaus Brockhaus, Apr 05 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 (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).

Formula

G.f.: (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)/(105*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

Mathematica

coxG[{21, 105, -14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2024 *)

Crossrefs

Cf. A170735 (G.f.: (1+x)/(1-15*x)).

Sequence in context: A168741 A168789 A168837 * A168933 A168981 A169029

Adjacent sequences: A168882 A168883 A168884 * A168886 A168887 A168888

Keyword

nonn

Author

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

Status

approved