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

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

Offset

1,2

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

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, King Graph

Formula

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

Crossrefs

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

Cf. A288033, A140518, A158651.

Sequence in context: A220731 A239403 A254607 * A362541 A268055 A268078

Adjacent sequences: A236687 A236688 A236689 * A236691 A236692 A236693

Keyword

nonn,hard

Author

Jaimal Ichharam, Jan 30 2014

Extensions

a(5) from Jaimal Ichharam, Feb 12 2014

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

Status

approved