A169407 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690

Offset

0,2

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 45. - Klaus Brockhaus, Jun 27 2011

Computed with Magma using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).

Formula

G.f.: (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)/(36*t^32 - 8*t^31 - 8*t^30 - 8*t^29 - 8*t^28 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22 - 8*t^21 - 8*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-8*sum(k=1..31, x^k)+36*x^32).

Mathematica

coxG[{32, 36, -8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 23 2016 *)

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*x) ).

Sequence in context: A169263 A169311 A169359 * A169455 A169503 A169551

Adjacent sequences: A169404 A169405 A169406 * A169408 A169409 A169410

Keyword

nonn

Author

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

Status

approved