A168927 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = 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 at index 22: a(22) = 1094189891315123592045, A003952(22) = 1094189891315123592090. - Klaus Brockhaus, Apr 09 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, -36).

Formula

G.f.: (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^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).

Mathematica

coxG[{22, 36, -8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 11 2015 *)

Crossrefs

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

Sequence in context: A168783 A168831 A168879 * A168975 A169023 A169071

Adjacent sequences: A168924 A168925 A168926 * A168928 A168929 A168930

Keyword

nonn

Author

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

Status

approved