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A163549
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
1
1, 29, 812, 22736, 636608, 17824618, 499077936, 13973864310, 391259299536, 10955011154976, 306733334006862, 8588337963333660, 240467992209756738, 6732950603977585764, 188518328027869860720, 5278393098774299901978
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170748, 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)/(378*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
a(n) = 27*a(n-1)+27*a(n-2)+27*a(n-3)+27*a(n-4)-378*a(n-5). - Wesley Ivan Hurt, May 11 2021
MATHEMATICA
CoefficientList[Series[(1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 378, -27}] (* 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)/(1-28*x+405*x^5-378*x^6)) \\ G. C. Greubel, Jul 27 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6) )); // G. C. Greubel, May 16 2019
(Sage) ((1+x)*(1-x^5)/(1-28*x+405*x^5-378*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
CROSSREFS
Sequence in context: A159669 A162831 A163207 * A164026 A164665 A164974
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved