A170358 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = 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, 11, 11, 11, -66).

Formula

G.f. (t^43 + 2*t^42 + 2*t^41 + 2*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^43 - 11*t^42 - 11*t^41 - 11*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[42]]+t^43+1, den=Total[-11 t^Range[42]]+66t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, May 29 2013 *)

Crossrefs

Sequence in context: A170214 A170262 A170310 * A170406 A170454 A170502

Adjacent sequences: A170355 A170356 A170357 * A170359 A170360 A170361

Keyword

nonn

Author

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

Status

approved