A163290 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 50, 2450, 120050, 5881225, 288120000, 14114940000, 691488000000, 33875854559400, 1659571130851200, 81302047554268800, 3982970548016611200, 195124905996721243200, 9559128916780140902400, 468299754871670360217600

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170769, although the two sequences are eventually different.

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

Links

• Index entries for linear recurrences with constant coefficients, signature (48, 48, 48, -1176).

Programs

Mathematica

CoefficientList[Series[(t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1), {t,0,50}], t] (* or *) Join[{1}, LinearRecurrence[ {48,48,48,-1176}, {50, 2450, 120050, 5881225}, 25]] (* G. C. Greubel, Dec 17 2016 *)
coxG[{4,1176,-48}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 22 2020 *)

PARI

Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1) + O(t^50)) \\ G. C. Greubel, Dec 17 2016

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1176*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).