This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A268446 Number of North-East lattice paths from (0,0) to (n,n) that cross the diagonal y = x horizontally exactly three times. 2
 1, 14, 119, 798, 4655, 24794, 123970, 592020, 2731365, 12271350, 53993940, 233646504, 997490844, 4211628008, 17620076360, 73153696336, 301758997386, 1237956266316, 5054988087457, 20558563992050, 83322650532485, 336691526641470, 1356968880100470, 5456577564869340, 21898107332699325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,2 COMMENTS It is related to paired pattern P_3 in Section 3.3 in Pan and Remmel's link. LINKS G. C. Greubel, Table of n, a(n) for n = 6..1000 Daniel Birmajer, Juan B. Gil, Michael D. Weiner, Bounce statistics for rational lattice paths, arXiv:1707.09918 [math.CO], 2017, p. 9. Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016. FORMULA G.f.: -((2*(2*x + f(x) - 1)^3)/(-2*x + f(x) +1)^4), where f(x) = sqrt(1 - 4*x). From Karol A. Penson, Nov 19 2016: (Start) a(n) = 14*binomial(2*n+13,n)/(n+14). G.f.: 4^7/(1+sqrt(1-4*z))^14. E.g.f.(in Maple notation): hypergeom([7,15/2],[1,15],4*z). Recurrence: (-4*n^2-66*n-272)*a(n+1)+(n^2+18*n+32)*a(n+2)=0, for n>=0, a(0)=1, a(1)=14. Asymptotics: (114688*n-6838272)*4^n*sqrt(1/n)/(sqrt(Pi)*n^2). (End) MAPLE seq(14*binomial(2*n+13, n)/(n+14), n=0..25); MATHEMATICA Rest[Rest[Rest[Rest[Rest[Rest[CoefficientList[Series[-((2 (2 x + Sqrt[1 - 4 x] - 1)^3) / (-2 x + Sqrt[1 - 4 x] + 1)^4), {x, 0, 33}], x]]]]]]] (* Vincenzo Librandi, Feb 06 2016 *) PROG (PARI) for(n=0, 25, print1(14*binomial(2*n+13, n)/(n+14), ", ")) \\ G. C. Greubel, Apr 09 2017 CROSSREFS Sequence in context: A023012 A073383 A022642 * A221230 A240051 A202072 Adjacent sequences:  A268443 A268444 A268445 * A268447 A268448 A268449 KEYWORD nonn AUTHOR Ran Pan, Feb 04 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 18 05:48 EST 2018. Contains 318215 sequences. (Running on oeis4.)