A145603 - OEIS

A145603

a(n) is the number of walks from (0,0) to (0,4) that remain in the upper half-plane y >= 0 using 2*n +2 unit steps either up (U), down (D), left (L) or right (R).

1, 35, 720, 12375, 196625, 3006003, 45048640, 668144880, 9859090500, 145173803500, 2136958387520, 31479019635375, 464342770607625, 6861343701121875, 101583106970400000, 1507019252941540800

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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 A145602. This sequence is the central column taken from the triangle A145599, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 4.

LINKS

Table of n, a(n) for n=1..16.

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

FORMULA

a(n) = 5/(2*n+3)*binomial(2*n+3,n+4)*binomial(2*n+3,n-1).

MAPLE

with(combinat):

a(n) = 5/(2*n+3)*binomial(2*n+3, n+4)*binomial(2*n+3, n-1);

seq(a(n), n = 1..19);

CROSSREFS

A000891, A145599, A145600, A145601, A145602.

Sequence in context: A140405 A367250 A278361 * A326865 A139641 A240928

Adjacent sequences: A145600 A145601 A145602 * A145604 A145605 A145606

KEYWORD

easy,nonn

AUTHOR

Peter Bala, Oct 15 2008

STATUS

approved