A170214 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784

Offset

0,2

Comments

The initial terms coincide with those of A170732, 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..16.

Index entries for linear recurrences with constant coefficients, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

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)/(66*t^40 - 11*t^39 - 11*t^38 - 11*t^37 - 11*t^36 - 11*t^35 - 11*t^34

- 11*t^33 - 11*t^32 - 11*t^31 - 11*t^30 - 11*t^29 - 11*t^28 - 11*t^27 -

11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 -

11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 -

11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5

- 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1)

Mathematica

With[{num=Total[2t^Range[39]]+t^40+1, den=Total[-11 t^Range[39]]+ 66t^40+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jun 28 2012 *)

Crossrefs

Sequence in context: A170070 A170118 A170166 * A170262 A170310 A170358

Adjacent sequences: A170211 A170212 A170213 * A170215 A170216 A170217

Keyword

nonn

Author

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

Status

approved