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A011795
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Floor(C(n,4)/5).
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6
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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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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory
Index entries for sequences related to Lyndon words
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1,1,-4,6,-4,1).
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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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seq(floor(binomial(n, 4)/5), n=0.. 40); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 12 2009]
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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 *)
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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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Cf. A000031, A001037, A051168. Same as A051170(n+1).
A column of triangle A011847.
Sequence in context: A004006 A089240 A057524 * A051170 A193911 A206417
Adjacent sequences: A011792 A011793 A011794 * A011796 A011797 A011798
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, David Broadhurst
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STATUS
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approved
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