A236690 -id:A236690 - cp's OEIS frontend

A288033 Number of (undirected) paths in the n X n king graph.

0, 30, 5148, 6014812, 57533191444, 4956907379126694, 3954100866385811897908, 29986588563791584765930866780, 2187482261973324160097873804506155572, 1550696105068168200375810546149511240714556526

Offset: 1

Eric W. Weisstein, Jun 04 2017

Paths of length zero are not counted here. - Andrew Howroyd, Jun 10 2017

Eric Weisstein's World of Mathematics, Graph Path
Eric Weisstein's World of Mathematics, King Graph

Cf. A236690, A288032, A288148, A234622, A158651, A140519.

a(5)-a(10) from Andrew Howroyd, Jun 10 2017

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

Original entry on oeis.org

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

Offset: 1

Jaimal Ichharam, Jan 30 2014

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

			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

Cf. A236690 (includes diagonal edges).

Cf. A288032, A007764, A121785, A120443.

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

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

cp's OEIS Frontend

A288033 Number of (undirected) paths in the n X n king graph.

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