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A011795
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a(n) = floor(C(n,4)/5).
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7
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0, 0, 0, 0, 0, 1, 3, 7, 14, 25, 42, 66, 99, 143, 200, 273, 364, 476, 612, 775, 969, 1197, 1463, 1771, 2125, 2530, 2990, 3510, 4095, 4750, 5481, 6293, 7192, 8184, 9275, 10472, 11781, 13209, 14763, 16450, 18278
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OFFSET
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0,7
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COMMENTS
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a(n-1)=number of aperiodic necklaces (Lyndon words) with 5 black beads and n-5 white beads.
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REFERENCES
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J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 147.
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LINKS
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FORMULA
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G.f.: x^5(1+x^3)/((1-x)^3(1-x^2)(1-x^5)) = x^5*(1-x+x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)).
a(n) = floor(binomial(n+1,5)/(n+1)). - Gary Detlefs, Nov 23 2011
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MAPLE
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MATHEMATICA
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CoefficientList[Series[x^5(1+x^3)/((1-x)^3(1-x^2)(1-x^5))=x^5*(1-x+x^2)/((1-x)^5*(1+x+x^2+x^3+x^4)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 19 2012 *)
CoefficientList[Series[x^4/5 (1/(1-x)^5-1/(1- x^5)), {x, 0, 50}], x] (* Herbert Kociemba, Oct 16 2016 *)
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PROG
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(Magma) [Floor(Binomial(n+1, 5)/(n+1)): n in [0..45]]; // Vincenzo Librandi Jun 19 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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