A170074 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = 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

Vincenzo Librandi, Table of n, a(n) for n = 0..800

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, -120).

Formula

G.f. (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^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[36]]+t^37+1, den=Total[-15 t^Range[36]]+120t^37+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 03 2013 *)

Crossrefs

Sequence in context: A169510 A169558 A170026 * A170122 A170170 A170218

Adjacent sequences: A170071 A170072 A170073 * A170075 A170076 A170077

Keyword

nonn

Author

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

Status

approved