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A165782
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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.
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1
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1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543851, 423262980, 2539577145, 15237458460, 91424724300, 548548187040, 3291288169680, 19747723302720, 118486305524160, 710917627392000, 4265504529834660
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (5,5,5,5,5,5,5,5,5,-15).
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FORMULA
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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).
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1-6*t+15*t^10-6*t^11) ).list()
(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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