A169222 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = 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 28: a(28) = 5516815412193254355313652349796216, A170736(28) = 5516815412193254355313652349796352. - Klaus Brockhaus, May 24 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, -120).

Formula

G.f.: (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^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).

a(n) = -120*a(n-28) + 15*Sum_{k=1..27} a(n-k). - Wesley Ivan Hurt, Mar 01 2023

Mathematica

coxG[{28, 120, -15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 12 2019 *)

Crossrefs

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

Sequence in context: A169078 A169126 A169174 * A169270 A169318 A169366

Adjacent sequences: A169219 A169220 A169221 * A169223 A169224 A169225

Keyword

nonn

Author

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

Status

approved