A169314 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622784

Offset

0,2

Comments

The initial terms coincide with those of A170732, although the two sequences are eventually different.

First disagreement at index 30: a(30) = 257157673283083956856362815717298, A170732(30) = 257157673283083956856362815717376. - Klaus Brockhaus, Jun 22 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 (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).

Formula

G.f.: (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)/(66*t^30 - 11*t^29 - 11*t^28 - 11*t^27 - 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).

Mathematica

coxG[{30, 66, -11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 25 2015 *)

Crossrefs

Cf. A170732 (G.f.: (1+x)/(1-12*x)).

Sequence in context: A169170 A169218 A169266 * A169362 A169410 A169458

Adjacent sequences: A169311 A169312 A169313 * A169315 A169316 A169317

Keyword

nonn

Author

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

Status

approved