A169403 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343750, 11718750, 58593750, 292968750, 1464843750, 7324218750, 36621093750, 183105468750, 915527343750, 4577636718750, 22888183593750, 114440917968750, 572204589843750

Offset

0,2

Comments

The initial terms coincide with those of A003948, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 15. - 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..165

Index entries for linear recurrences with constant coefficients, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).

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

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-4*sum(k=1..31,x^k)+10*x^32).

Prog

(PARI) x='x+O('x^66); /* that many terms */
Vec((1+2*sum(k=1, 31, x^k)+x^32)/(1-4*sum(k=1, 31, x^k)+10*x^32)) /* show terms */
/* Joerg Arndt, Jun 26 2011 */

Crossrefs

Cf. A003948 (G.f.: (1+x)/(1-5*x) ).

Sequence in context: A169259 A169307 A169355 * A169451 A169499 A169547

Adjacent sequences: A169400 A169401 A169402 * A169404 A169405 A169406

Keyword

nonn

Author

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

Status

approved