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A163995
Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 26, 650, 16250, 406250, 10156250, 253905925, 6347640000, 158690797200, 3967264860000, 99181494750000, 2479534200000000, 61988275781355300, 1549704914070300000, 38742573340231207200, 968563095719204700000, 24214046448355276500000, 605350387594249537500000
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^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).
a(n) = -300*a(n-6) + 24*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 24 2017 *)
coxG[{6, 300, -24}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 13 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7)) \\ G. C. Greubel, Aug 24 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7) )); // G. C. Greubel, Aug 13 2019
(Sage)
def A163995_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-25*t+324*t^6-300*t^7)).list()
A163995_list(30) # G. C. Greubel, Aug 13 2019
(GAP) a:=[26, 650, 16250, 406250, 10156250, 253905925];; for n in [7..30] do a[n]:=24*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -300*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019
CROSSREFS
Sequence in context: A162812 A163177 A163526 * A164639 A164964 A165369
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved