A170209 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset

0,2

Comments

The initial terms coincide with those of A003950, 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..19.

Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Formula

G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*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)/(21*t^40 - 6*t^39 - 6*t^38 - 6*t^37 - 6*t^36 - 6*t^35 - 6*t^34 -

6*t^33 - 6*t^32 - 6*t^31 - 6*t^30 - 6*t^29 - 6*t^28 - 6*t^27 - 6*t^26 -

6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 -

6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 -

6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1)

Mathematica

coxG[{40, 21, -6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 14 2019 *)

Crossrefs

Sequence in context: A170065 A170113 A170161 * A170257 A170305 A170353

Adjacent sequences: A170206 A170207 A170208 * A170210 A170211 A170212

Keyword

nonn

Author

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

Status

approved