A169406 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799488, 2533274790395904, 20266198323167232, 162129586585337856

Offset

0,2

Comments

The initial terms coincide with those of A003951, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 36. - Klaus Brockhaus, Jun 27 2011

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

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).

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

G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-7*sum(k=1..31, x^k)+28*x^32).

Mathematica

With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-7 t^Range[31]]+ 28t^32+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Oct 21 2011 *)

Crossrefs

Cf. A003951 (G.f.: (1+x)/(1-8*x) ).

Sequence in context: A169262 A169310 A169358 * A169454 A169502 A169550

Adjacent sequences: A169403 A169404 A169405 * A169407 A169408 A169409

Keyword

nonn

Author

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

Status

approved