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A163527
Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 27, 702, 18252, 474552, 12338001, 320778900, 8340014475, 216834216300, 5637529462500, 146571601954050, 3810753388040625, 99076773337132500, 2575922925294444375, 66972093393463976250, 1741224960366454777500
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170746, 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)/(325*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
a(n) = 25*a(n-1)+25*a(n-2)+25*a(n-3)+25*a(n-4)-325*a(n-5). - Wesley Ivan Hurt, May 10 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 325, -25}] (* 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)/(1-26*x+350*x^5-325*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-26*x+350*x^5-325*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A342037 A162827 A163179 * A164017 A164644 A164969
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved