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A165782
Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
1
1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851, 423262980, 2539577145, 15237458460, 91424724300, 548548187040, 3291288169680, 19747723302720, 118486305524160, 710917627392000, 4265504529834660
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003949, although the two sequences are eventually different.
Computed with Magma using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^10 - 5*t^9 - 5*t^8 - 5*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).
MAPLE
seq(coeff(series((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 22 2019
MATHEMATICA
CoefficientList[Series[(1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 15, -5}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)
PROG
(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11)) \\ G. C. Greubel, Aug 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) )); // G. C. Greubel, Sep 22 2019
(SageMath)
def A165782_list(prec):
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) ).list()
A165782_list(30) # G. C. Greubel, Sep 22 2019
(GAP) a:=[7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851];; for n in [11..30] do a[n]:=5*Sum([1..9], j-> a[n-j]) -15*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019
CROSSREFS
Sequence in context: A164369 A164742 A165214 * A166365 A166518 A166878
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved