A236690 - OEIS

%I #41 Feb 16 2025 08:33:21

%S 1,64,10305,12029640,115066382913,9913814758253424,

%T 7908201732771623795865,59973177127583169531861733624,

%U 4374964523946648320195747609012311225,3101392210136336400751621092299022481429113152

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

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

%C 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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>

%F a(n) = 2*A288033(n) + n^2. - _Andrew Howroyd_, Jun 10 2017

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

%Y Cf. A288033, A140518, A158651.

%K nonn,hard,changed

%O 1,2

%A _Jaimal Ichharam_, Jan 30 2014

%E a(5) from _Jaimal Ichharam_, Feb 12 2014

%E Named edited and a(6)-a(10) from _Andrew Howroyd_, May 12 2017