A169405 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset

0,2

Comments

The initial terms coincide with those of A003950, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 28. - Klaus Brockhaus, Jun 26 2011

Computed with Magma using commands similar to those used to compute A154638.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Formula

G.f.: (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)/(21*t^32 - 6*t^31 - 6*t^30 - 6*t^29 - 6*t^28 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-6*sum(k=1..31,x^k)+21*x^32).

Mathematica

With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-6 t^Range[31]]+21t^32+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 27 2012 *)

Prog

(PARI) x='x+O('x^66); /* that many terms */
Vec((1+2*sum(k=1, 31, x^k)+x^32)/(1-6*sum(k=1, 31, x^k)+21*x^32))   /* show terms */
/* Joerg Arndt, Jun 26 2011 */

Crossrefs

Cf. A003950 (G.f.: (1+x)/(1-7*x) ).

Sequence in context: A169261 A169309 A169357 * A169453 A169501 A169549

Adjacent sequences: A169402 A169403 A169404 * A169406 A169407 A169408

Keyword

nonn,easy

Author

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

Status

approved