

A236690


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


2



1, 64, 10305, 12029640, 115066382913, 9913814758253424, 7908201732771623795865, 59973177127583169531861733624, 4374964523946648320195747609012311225, 3101392210136336400751621092299022481429113152
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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 * A268055 A268078 A202548
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



