A170391 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750

Offset

0,2

Comments

The initial terms coincide with those of A170765, 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 (44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, -990).

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)/(990*t^43 - 44*t^42 - 44*t^41 - 44*t^40 - 44*t^39 -

44*t^38 - 44*t^37 - 44*t^36 - 44*t^35 - 44*t^34 - 44*t^33 - 44*t^32 -

44*t^31 - 44*t^30 - 44*t^29 - 44*t^28 - 44*t^27 - 44*t^26 - 44*t^25 -

44*t^24 - 44*t^23 - 44*t^22 - 44*t^21 - 44*t^20 - 44*t^19 - 44*t^18 -

44*t^17 - 44*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 -

44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 -

44*t^2 - 44*t + 1)

Mathematica

With[{num=Total[2t^Range[42]]+t^43+1, den=Total[-44 t^Range[42]]+ 990t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jun 21 2012 *)

Crossrefs

Sequence in context: A170247 A170295 A170343 * A170439 A170487 A170535

Adjacent sequences: A170388 A170389 A170390 * A170392 A170393 A170394

Keyword

nonn

Author

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

Status

approved