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 A005221 Number of Dyck paths of knight moves. (Formerly M2371) 0
 0, 0, 1, 1, 3, 4, 12, 22, 61, 128, 335, 756, 1936, 4580, 11652, 28402, 72209, 179460, 457274, 1151725, 2945129, 7489680, 19228598, 49256157, 126958030, 327072560, 846173899, 2190012371, 5685200054, 14770728584, 38463268482, 100259225816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES J. Labelle and Y.-N. Yeh, Dyck paths of knight moves, Discrete Applied Math., 24 (1989), 213-221. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS FORMULA G.f.: z^2*A^2/(1-z*A), where A=(1+2*z+sqrt(1-4*z+4*z^2-4*z^4)-sqrt(2)*sqrt(1-4*z^2-2*z^4+(2*z+1)*sqrt(1-4*z+4*z^2-4*z^4)))/(4*z^2). MATHEMATICA a = (2*z + Sqrt[-4*z^4 + 4*z^2 - 4*z + 1] - Sqrt[2]*Sqrt[-2*z^4 - 4*z^2 + (2*z + 1)*Sqrt[-4*z^4 + 4*z^2 - 4*z + 1] + 1] + 1)/(4*z^2); gf = z^2*a^2/(1 - z*a); CoefficientList[Series[gf, {z, 0, 31}], z](* Jean-François Alcover, Dec 21 2012, from g.f.*) CROSSREFS Sequence in context: A075220 A075221 A129922 * A000206 A075223 A071332 Adjacent sequences:  A005218 A005219 A005220 * A005222 A005223 A005224 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Emeric Deutsch, Dec 17 2003 STATUS approved

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