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A163526
Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 26, 650, 16250, 406250, 10155925, 253890000, 6347047200, 158671110000, 3966651000000, 99163106355300, 2478998445300000, 61972980856207200, 1549275016079700000, 38730637808401500000, 968235006358878382800
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170745, 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)/(300*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
a(n) = 24*a(n-1)+24*a(n-2)+24*a(n-3)+24*a(n-4)-300*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 300, -24}] (* 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)/(1-25*x+324*x^5-300*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-25*x+324*x^5-300*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A106793 A162812 A163177 * A163995 A164639 A164964
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved