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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..14.

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

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

Adjacent sequences:  A163287 A163288 A163289 * A163291 A163292 A163293

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)