A236753 Number of simple (non-intersecting) directed paths on the grid graph P_n X P_n.

1, 28, 653, 28512, 3060417, 873239772, 687430009069, 1532025110398168, 9829526954625359697, 183563561823425961932572, 10056737067604248527218979485, 1626248896102138091401810358337184

Offset

1,2

Comments

This is the number of directed paths on P_n X P_n of any length and also includes one zero length path per vertex. - Andrew Howroyd, May 27 2017

Links

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

Formula

a(n) = 2*A288032(n) + n^2. - Andrew Howroyd, Jun 10 2017

Example

For n=2 there are 4 zero length paths (one for each vertex), 8 paths with 1 one edge, 8 paths with 2 edges and 8 paths with 3 edges, so a(2)=28. - Andrew Howroyd, May 27 2017

Crossrefs

Cf. A236690 (includes diagonal edges).

Cf. A288032, A007764, A121785, A120443.

Sequence in context: A184329 A070310 A309804 * A269473 A278805 A160141

Adjacent sequences: A236750 A236751 A236752 * A236754 A236755 A236756

Keyword

nonn,hard,more

Author

Jaimal Ichharam, Jan 30 2014

Extensions

a(6) corrected and a(8) added from Jaimal Ichharam, Feb 13 2014

a(6)-a(8) corrected and a(9)-a(12) from Andrew Howroyd, May 27 2017

Status

approved