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A163954
Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
1
1, 10, 90, 810, 7290, 65610, 590445, 5313600, 47818800, 430336800, 3872739600, 34852032000, 313644670380, 2822589491040, 25401392681760, 228595320793440, 2057202978723360, 18513432737727840, 166608348947205840
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003952, 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)/(36*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
a(n) = -36*a(n-6) + 8*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021
MAPLE
seq(coeff(series((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)) \\ G. C. Greubel, Aug 13 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7) )); // G. C. Greubel, Aug 10 2019
(Sage)
def A163954_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)).list()
A163954_list(30) # G. C. Greubel, Aug 10 2019
(GAP) a:=[10, 90, 810, 7290, 65610, 590445];; for n in [7..30] do a[n]:=8*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -36*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019
CROSSREFS
Sequence in context: A010576 A162983 A163397 * A164548 A164779 A165219
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved