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 A268447 Number of North-East lattice paths from (0,0) to (n,n) that cross the diagonal y = x horizontally exactly four times. 0
 1, 18, 189, 1518, 10350, 63180, 356265, 1893294, 9612108, 47071640, 223926516, 1040310648, 4739192952, 21238169904, 93865125915, 409972529754, 1772528290407, 7596549816030, 32308782859535, 136496564854650, 573285572389530, 2395339717603140, 9962435643667605 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,2 COMMENTS It is related to paired pattern P_3 in Section 3.3 in Pan and Remmel's link. LINKS Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016. FORMULA G.f.: (2*(-1 + f(x) + 2*x)^4)/(1 + f(x) - 2*x)^5, where f(x) = sqrt(1 - 4*x). Conjecture: -(n+10)*(n-8)*a(n) +2*n*(2*n+1)*a(n-1)=0. - R. J. Mathar, Jun 07 2016 MATHEMATICA Rest[Rest[Rest[Rest[Rest[Rest[Rest[Rest[CoefficientList[Series[(2 (-1 + Sqrt[1 - 4 x] + 2 x)^4) / (1 + Sqrt[1 - 4 x] - 2 x)^5, {x, 0, 33}], x]]]]]]]]] (* Vincenzo Librandi, Feb 06 2016 *) PROG (PARI) x='x+O('x^100); Vec((2*(-1 + (1 - 4*x)^(1/2) + 2*x)^4)/(1 + (1 - 4*x)^(1/2) - 2*x)^5) \\ Altug Alkan, Feb 04 2016 CROSSREFS Cf. A268446. Sequence in context: A073385 A036219 A022646 * A259163 A004314 A338099 Adjacent sequences:  A268444 A268445 A268446 * A268448 A268449 A268450 KEYWORD nonn AUTHOR Ran Pan, Feb 04 2016 STATUS approved

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Last modified January 24 04:47 EST 2022. Contains 350534 sequences. (Running on oeis4.)