A145602 a(n) is the number of walks from (0,0) to (0,3) that remain in the upper half-plane y >= 0 using 2*n +1 unit steps either up (U), down (D), left (L) or right (R).

1, 24, 392, 5760, 81675, 1145144, 16032016, 225059328, 3173688180, 44986664800, 641087516256, 9183622822400, 132211882468575, 1912322889603000, 27781440618420000, 405248874740582400, 5933888308457316900

Offset

1,2

Comments

Cf. A000891, which enumerates walks in the upper half-plane starting and finishing at the origin. See also A145600, A145601 and A145603. This sequence is the central column taken from the triangle A145598, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 3.

Links

Table of n, a(n) for n=1..17.

R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6

Formula

a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1).

Maple

with(combinat):
a(n) = 2/(n+1)*binomial(2*n+2, n+3)*binomial(2*n+2, n-1);
seq(a(n), n = 1..19);

Crossrefs

A000891, A145598, A145600, A145601, A145603.

Sequence in context: A022448 A025947 A007752 * A020447 A021894 A021694

Adjacent sequences: A145599 A145600 A145601 * A145603 A145604 A145605

Keyword

easy,nonn

Author

Peter Bala, Oct 15 2008

Status

approved