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 A086905 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(k,floor(k/2)). 3
 1, 0, 2, 1, 5, 5, 15, 20, 50, 76, 176, 286, 638, 1078, 2354, 4081, 8789, 15521, 33099, 59279, 125477, 227239, 478193, 873885, 1830271, 3370029, 7030571, 13027729, 27088871, 50469889, 104647631, 195892564, 405187826, 761615284, 1571990936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Knödel walks starting and ending at 0, with n steps. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 H. Prodinger, The Kernel Method: a collection of examples, Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp. FORMULA G.f.: (sqrt((1+2*x)/(1-2*x))-1)/2/x/(1+x). a(n) ~ 2^(n+3/2) / (3*sqrt(Pi*n)) * (1 - 2/(3*n)+ 3*(-1)^n/(4*n)). - Vaclav Kotesovec, Mar 02 2014 MATHEMATICA Table[Sum[(-1)^(n-k)*Binomial[k, Floor[k/2]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *) PROG (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k, k\2)); \\ Michel Marcus, Dec 04 2016 CROSSREFS Cf. A036256, A001405. First column of triangle A101491. Sequence in context: A119245 A128731 A129157 * A167638 A317878 A209108 Adjacent sequences:  A086902 A086903 A086904 * A086906 A086907 A086908 KEYWORD nonn AUTHOR Vladeta Jovovic, Sep 19 2003 STATUS approved

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Last modified October 23 18:52 EDT 2018. Contains 316530 sequences. (Running on oeis4.)