A169493 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = 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.

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, 46, -1081).

Formula

G.f. (t^33 + 2*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^33 - 46*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)

Mathematica

coxG[{33, 1081, -46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 19 2016 *)

Crossrefs

Sequence in context: A169349 A169397 A169445 * A169541 A170009 A170057

Adjacent sequences: A169490 A169491 A169492 * A169494 A169495 A169496

Keyword

nonn

Author

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

Status

approved