A169404 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472

Offset

0,2

Comments

The initial terms coincide with those of A003949, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 21. - 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 (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

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

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-5*sum(k=1..31,x^k)+15*x^32).

Mathematica

coxG[{32, 15, -5}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 21 2020 *)

Prog

(PARI) x='x+O('x^66); /* that many terms */
Vec((1+2*sum(k=1, 31, x^k)+x^32)/(1-5*sum(k=1, 31, x^k)+15*x^32))   /* show terms */
/* Joerg Arndt, Jun 26 2011 */

Crossrefs

Cf. A003949 (G.f.: (1+x)/(1-6*x) ).

Sequence in context: A169260 A169308 A169356 * A169452 A169500 A169548

Adjacent sequences: A169401 A169402 A169403 * A169405 A169406 A169407

Keyword

nonn,easy

Author

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

Status

approved