A236690 Number of simple directed paths on an n X n king graph.

1, 64, 10305, 12029640, 115066382913, 9913814758253424, 7908201732771623795865, 59973177127583169531861733624, 4374964523946648320195747609012311225, 3101392210136336400751621092299022481429113152

Offset: 1

Author

Jaimal Ichharam, Jan 30 2014

Keywords

• nonn
• hard

Comments

This is the number (assuming each character is unique) of strings that are possible in an n X n Boggle grid.

This sequence gives the number of directed paths. Paths may start and end on any vertex and may be of any length. Paths of length zero are counted here. - Andrew Howroyd, May 12 2017

Links

• Eric Weisstein's World of Mathematics, King Graph

Crossrefs

Cf. A236753 for a simpler version of the problem without diagonal edges.

Cf. A288033, A140518, A158651.

Formula

a(n) = 2*A288033(n) + n^2. - Andrew Howroyd, Jun 10 2017

Extensions

a(5) from Jaimal Ichharam, Feb 12 2014

Named edited and a(6)-a(10) from Andrew Howroyd, May 12 2017