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A163525
Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 25, 600, 14400, 345600, 8294100, 199051200, 4777056300, 114645211200, 2751385708800, 66030872460900, 1584683711924400, 38031035684483100, 912711895976984400, 21904294481198985600, 525684083700365474100
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.
FORMULA
G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
a(n) = 23*a(n-1)+23*a(n-2)+23*a(n-3)+23*a(n-4)-276*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 276, -23}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)
PROG
(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-24*x+299*x^5-276*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A104643 A162811 A163175 * A163993 A164638 A164963
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved