login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=2..30.

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-Fran├žois 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

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 13:54 EST 2019. Contains 319306 sequences. (Running on oeis4.)