A170224 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512

Offset

0,2

Comments

The initial terms coincide with those of A170742, 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..15.

Index entries for linear recurrences with constant coefficients, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231)

Formula

G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*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)/(231*t^40 - 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 - 21*t^35 - 21*t^34

- 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 -

21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 -

21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 -

21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5

- 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)

Mathematica

With[{num=Total[2t^Range[39]]+t^40+1, den=Total[-21 t^Range[39]]+ 231t^40+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 17 2012 *)

Crossrefs

Sequence in context: A170080 A170128 A170176 * A170272 A170320 A170368

Adjacent sequences: A170221 A170222 A170223 * A170225 A170226 A170227

Keyword

nonn

Author

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

Status

approved