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 A011797 a(n) = floor(C(n,6)/7). 7
 0, 0, 0, 0, 0, 0, 0, 1, 4, 12, 30, 66, 132, 245, 429, 715, 1144, 1768, 2652, 3876, 5537, 7752, 10659, 14421, 19228, 25300, 32890, 42287, 53820, 67860, 84825, 105183, 129456, 158224, 192129, 231880, 278256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS a(n-1) is the number of aperiodic necklaces (Lyndon words) with 7 black beads and n-7 white beads. LINKS D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, arXiv:hep-th/9604128, 1996. FORMULA G.f.: (1+x^3)^2/((1-x)^4(1-x^2)^2(1-x^7))*x^7. a(n) = floor(binomial(n+1,7)/(n+1)). [Gary Detlefs, Nov 23 2011] G.f.: (x^6/7)*(1/(1-x)^7-1/(1- x^7)). - Herbert Kociemba, Oct 16 2016 MATHEMATICA CoefficientList[Series[x^6/7 (1/(1-x)^7-1/(1- x^7)), {x, 0, 40}], x]; (* Herbert Kociemba, Oct 16 2016 *) PROG (PARI) a(n) = binomial(n, 6)\7; \\ Michel Marcus, Oct 16 2016 CROSSREFS Cf. A000031, A001037, A051168. Same as A051172(n+1). First differences of A011853. A column of triangle A011847. Sequence in context: A166213 A274250 A004036 * A051172 A032192 A212587 Adjacent sequences:  A011794 A011795 A011796 * A011798 A011799 A011800 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 23 04:40 EST 2019. Contains 319370 sequences. (Running on oeis4.)