OFFSET
0,3
COMMENTS
Number of lattice paths in the lattice [0..n] X [0..n] which do not pass through the point (floor(n/2),floor(n/2)). In this case, the "hole" in the lattice is at the point closest to the lattice center.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..200
Eric Weisstein's World of Mathematics, Lattice path.
FORMULA
Also, a(n) = Sum_{m=0..n} binomial(n, m)^2 - binomial(n, floor(n/2))^2.
G.f.: 1/sqrt(1-4*x) + 1/(4*x) - (4*x+1)*EllipticK(4*x)/(2*x*Pi). - Mark van Hoeij, May 01 2013
MAPLE
A071801:=n->binomial(2*n, n) - binomial(n, floor(n/2))^2: seq(A071801(n), n=0..30); # Wesley Ivan Hurt, Jan 03 2017
MATHEMATICA
Table[Binomial[2n, n] - Binomial[n, Floor[n/2]]^2, {n, 0, 20}]
PROG
(Magma) [Binomial(2*n, n) - Binomial(n, Floor(n/2))^2 : n in [0..40]]; // Wesley Ivan Hurt, Jan 03 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, Jun 06 2002
EXTENSIONS
More terms from Roger L. Bagula, Aug 28 2006
Edited by N. J. A. Sloane, Oct 08 2006
STATUS
approved