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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218321 Number of lattice paths from (0,0) to (n,n) which do not go above the diagonal x=y using steps (1,k), (k,1) with k>=0. 4
1, 2, 8, 39, 212, 1230, 7458, 46689, 299463, 1957723, 12996879, 87383754, 593794311, 4071599216, 28136612051, 195756911831, 1370068168916, 9639404836227, 68138551870047, 483682445360748, 3446462104490724, 24642148415136556, 176743014104068411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

Alois P. Heinz, Maple program for A218321

FORMULA

G.f.: (sqrt(x^4+4*x^3+2*x^2-8*x+1)+x^2+1-sqrt(2*(x^4+2*x^3-6*x^2-4*x+1+(x^2+1)*sqrt(x^4+4*x^3+2*x^2-8*x+1))))/(4*x^2). - Mark van Hoeij, Apr 17 2013

EXAMPLE

a(2) = 8: [(0,0),(1,0),(1,1),(2,1),(2,2)], [(0,0),(1,0),(1,1),(2,2)], [(0,0),(1,0),(2,0),(2,1),(2,2)], [(0,0),(1,0),(2,1),(2,2)], [(0,0),(1,0),(2,2)], [(0,0),(1,1),(2,1),(2,2)], [(0,0),(1,1),(2,2)], [(0,0),(2,1),(2,2)].

MAPLE

b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,

      add(b(x-i, y-1), i=0..x) +add(b(x-1, y-j), j=0..y) -b(x-1, y-1)))

    end:

a:= n-> b(n, n):

seq(a(n), n=0..30);

# second Maple program gives series:

series(RootOf(x^4*T^4-(x^2+1)*x^2*T^3-(x^2-2*x-2)*x*T^2-(x^2+1)*T+1, T), x=0, 31);  # Mark van Hoeij, Apr 17 2013

CROSSREFS

Cf. A082582, A168592, A263316.

Sequence in context: A112737 A206901 A162476 * A236339 A292100 A185650

Adjacent sequences:  A218318 A218319 A218320 * A218322 A218323 A218324

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 25 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 03:29 EDT 2018. Contains 316378 sequences. (Running on oeis4.)