A169366 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = 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.

First disagreement at index 31: a(31) = 22596875928343569839364720024765857656, A170736(31) = 22596875928343569839364720024765857792. - Klaus Brockhaus, Jun 17 2011

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, -120).

Formula

G.f.: (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^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).

Crossrefs

Cf. A170736 (G.f.: (1+x)/(1-16*x)).

Sequence in context: A169222 A169270 A169318 * A169414 A169462 A169510

Adjacent sequences: A169363 A169364 A169365 * A169367 A169368 A169369

Keyword

nonn

Author

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

Status

approved