A170026 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = 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, -120).

Formula

G.f. (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^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[35]]+t^36+1, den=Total[-15 t^Range[35]]+ 120t^36+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Nov 12 2011 *)

Crossrefs

Sequence in context: A169462 A169510 A169558 * A170074 A170122 A170170

Adjacent sequences: A170023 A170024 A170025 * A170027 A170028 A170029

Keyword

nonn

Author

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

Status

approved