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 A268429 Number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the right exactly once. 2
 1, 4, 16, 62, 238, 910, 3475, 13270, 50707, 193948, 742659, 2847126, 10928009, 41993692, 161555008, 622201838, 2398811962, 9257512318, 35760612784, 138263710226, 535038428936, 2072130742074, 8031333322206, 31151602276002, 120915026597458, 469648731423190, 1825348333058230, 7098811400187410, 27623655321103718 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link. By symmetry, a(n) is also the number of North-East lattice paths from (0,0) to (n,n) that bounce off the diagonal y = x to the left exactly once. LINKS Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016. FORMULA G.f.: (-1 + f(x) + 2*x)^2/(1 - f(x) + (-5 + f(x))*x)^2, where f(x) = sqrt(1 - 4*x). MATHEMATICA (1 - 4x + x^2 - 2x^3 - Sqrt[1-4x](1 - 2x - 3x^2))/(2(-1 + x(4+x))^2) + O[x]^31 // CoefficientList[#, x]& // Drop[#, 2]& (* Jean-François Alcover, Dec 15 2018 *) CROSSREFS Cf. A268407. Sequence in context: A250346 A085781 A113438 * A195339 A172025 A171278 Adjacent sequences:  A268426 A268427 A268428 * A268430 A268431 A268432 KEYWORD nonn AUTHOR Ran Pan, Feb 04 2016 STATUS approved

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Last modified October 21 14:10 EDT 2019. Contains 328301 sequences. (Running on oeis4.)