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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.
0
1, 50, 2450, 120050, 5881225, 288120000, 14114940000, 691488000000, 33875854559400, 1659571130851200, 81302047554268800, 3982970548016611200, 195124905996721243200, 9559128916780140902400, 468299754871670360217600
OFFSET
0,2
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.
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).
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 *)
PROG
(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
CROSSREFS
Sequence in context: A285877 A156087 A162919 * A163837 A164351 A164695
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved