A169461 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = 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.

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, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).

Formula

G.f. (t^33 + 2*t^32 + 2*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)/(105*t^33 - 14*t^32 - 14*t^31 - 14*t^30 - 14*t^29 - 14*t^28 - 14*t^27

- 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*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

With[{num=Total[2t^Range[32]]+t^33+1, den=Total[-14 t^Range[32]]+ 105t^33+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 03 2012 *)

Crossrefs

Sequence in context: A169317 A169365 A169413 * A169509 A169557 A170025

Adjacent sequences: A169458 A169459 A169460 * A169462 A169463 A169464

Keyword

nonn

Author

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

Status

approved