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A164026
Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 29, 812, 22736, 636608, 17825024, 499100266, 13974796080, 391293972342, 10956222324432, 306773975852064, 8589664345360896, 240510406272356430, 6734285904493468188, 188559852134231228994, 5279671570397554562148
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^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
a(n) = -378*a(n-6) + 27*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7), {t, 0, 30}], t] (* G. C. Greubel, Sep 07 2017 *)
coxG[{6, 378, -27}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 14 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)) \\ G. C. Greubel, Sep 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A164026_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-28*t+405*t^6-378*t^7)).list()
A164026_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[29, 812, 22736, 636608, 17825024, 499100266];; for n in [7..30] do a[n]:=27*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -378*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A162831 A163207 A163549 * A164665 A164974 A165512
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved