A170362 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398592

Offset

0,2

Comments

The initial terms coincide with those of A170736, 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 (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).

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)/(120*t^43 - 15*t^42 - 15*t^41 - 15*t^40 - 15*t^39 -

15*t^38 - 15*t^37 - 15*t^36 - 15*t^35 - 15*t^34 - 15*t^33 - 15*t^32 -

15*t^31 - 15*t^30 - 15*t^29 - 15*t^28 - 15*t^27 - 15*t^26 - 15*t^25 -

15*t^24 - 15*t^23 - 15*t^22 - 15*t^21 - 15*t^20 - 15*t^19 - 15*t^18 -

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

15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 -

15*t^2 - 15*t + 1)

Mathematica

With[{num=Total[2t^Range[42]]+t^43+1, den=Total[-15 t^Range[42]]+ 120t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, May 06 2012 *)

Crossrefs

Sequence in context: A170218 A170266 A170314 * A170410 A170458 A170506

Adjacent sequences: A170359 A170360 A170361 * A170363 A170364 A170365

Keyword

nonn

Author

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

Status

approved