

A236753


Number of simple (nonintersecting) directed paths on the grid graph P_n X P_n.


2



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



