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
Links
- Eric Weisstein's World of Mathematics, Lattice Path.
Programs
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Mathematica
Table[Factorial[6n]/Factorial[2n]^3-(Factorial[3n]/Factorial[n]^3)^2, {n, 1, 10}]
Formula
a(n) = s(3,2n)-s(3,n)^2.