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A164590
Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
1
1, 11, 110, 1100, 11000, 110000, 1100000, 10999945, 109998900, 1099983555, 10999781100, 109997266500, 1099967220000, 10999617750000, 109995633002970, 1099950885086625, 10999454401704780, 109993999528128375
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003953, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(45*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
a(n) = -45*a(n-7) + 9*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8), {t, 0, 30}], t] (* G. C. Greubel, Aug 12 2017 *)
coxG[{7, 45, -9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 28 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)) \\ G. C. Greubel, Aug 12 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8) )); // G. C. Greubel, Aug 28 2019
(Sage)
def A164590_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-10*t+54*t^7-45*t^8)).list()
A164590_list(30) # G. C. Greubel, Aug 28 2019
(GAP) a:=[11, 110, 1100, 11000, 110000, 1100000, 10999945];; for n in [8..30] do a[n]:=9*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -45*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019
CROSSREFS
Sequence in context: A163404 A115808 A163955 * A115806 A115830 A164780
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved