A071800 Number of lattice paths in the lattice [0..2n] X [0..2n] X [0..2n] which do not pass through the point (n,n,n). Number of paths through a lattice containing a "hole".

54, 26550, 14330736, 8264889270, 4978317147804, 3090501687886704, 1961313438507566400, 1265749551338006549430, 827693426702217868006500, 547017649101008848332870300, 364691794467483796757326646400, 244920478151771001164678945670000

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Eric Weisstein's World of Mathematics, Lattice Path.

Formula

a(n) = s(3,2n)-s(3,n)^2.

Mathematica

Table[Factorial[6n]/Factorial[2n]^3-(Factorial[3n]/Factorial[n]^3)^2, {n, 1, 10}]

Crossrefs

Cf. A006480, A071801, A071803.

Sequence in context: A030254 A085482 A084226 * A093254 A347061 A151635

Adjacent sequences: A071797 A071798 A071799 * A071801 A071802 A071803

Keyword

easy,nice,nonn

Author

T. D. Noe, Jun 06 2002

Status

approved