%I #33 May 23 2014 23:07:48

%S 1,1,2,12,54,100,330,1050,3024,8736,23220,62700,158004,406692,986986,

%T 2452450,5788640,14002560,32357052,76640148,174174520,405623400,

%U 909582212,2089064516,4633556448,10519464000,23120533800,51977741400,113365499940,252725219460,547593359850,1211884139250,2610998927040,5741708459520,12309472580460,26917328938500

%N a(n) = maximal number of shortest knight's move paths, from origin at center of an infinite open chessboard, to any square within n moves.

%C For n>4 this sequence is conjectured to be identical to A242511.

%C The same sequence results after replacing 'within n moves' with 'at shortest distance n moves'.

%D Fred Lunnon, Knights in Daze, to appear.

%H Fred Lunnon, <a href="/A242591/a242591.a.txt">Revised tables & functions for knight's path distance and count (MAGMA code)</a>

%e For n=5, there are 100 shortest paths of length 5 steps from (0,0) to (7,0); no square at 5 (or fewer) moves from the origin has more shortest paths.

%Y Cf. A242511, A242512, A242514, A183043, A242591.

%K easy,nonn,walk

%O 0,3

%A _Fred Lunnon_, May 16 2014 and May 18 2014