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A163993
Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
3
1, 25, 600, 14400, 345600, 8294400, 199065300, 4777560000, 114661267500, 2751866280000, 66044691360000, 1585070208000000, 38041627760729700, 912997692709095600, 21911911659905871900, 525885088676233035600
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170744, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
FORMULA
G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
G.f.: (1+x)*(1-x^7)/(1 -24*x +299*x^6 -276*x^7). - G. C. Greubel, Apr 25 2019
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7), {x, 0, 20}], x] (* G. C. Greubel, Aug 24 2017, modified Apr 25 2019 *)
coxG[{6, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 02 2018 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^7)/(1-24*x+299*x^6-276*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
CROSSREFS
Sequence in context: A162811 A163175 A163525 * A164638 A164963 A165368
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved