A169445 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696

Offset

0,2

Comments

The initial terms coincide with those of A170767, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 1128. - Klaus Brockhaus, Jun 30 2011

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

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).

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)/(1081*t^32 - 46*t^31 - 46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-46*sum(k=1..31,x^k)+1081*x^32).

Mathematica

With[{num=Total[2t^Range[31]]+t^32+1, den=Total[-46 t^Range[31]]+ 1081t^32+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Mar 17 2012 *)

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*x) ).

Sequence in context: A169301 A169349 A169397 * A169493 A169541 A170009

Adjacent sequences: A169442 A169443 A169444 * A169446 A169447 A169448

Keyword

nonn

Author

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

Status

approved