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a(n) is the maximal number of shortest knight's move paths, from origin at center of an infinite open chessboard, to square with coordinates <= n.
6

%I #32 Nov 24 2019 23:50:31

%S 1,12,54,54,54,54,85,240,240,588,1512,1512,3564,8700,8700,19965,47124,

%T 47124,105963,244244,244244,540540,1224080,1224080,2674984,5974956,

%U 5974956,12924522,28553200,28553200,61250490,134104432,134104432,285689624,620826672,620826672,1314933000,2839363800,2839363800,5984393805,12852021420,12852021420,26973910215,57655813500,57655813500,120569654700,256649540640,256649540640,535009931280,1134692142540,1134692142540,2358818719950,4986548028000,4986548028000,10340761857030,21796919253120,21796919253120,45102668144040,94821703158000,94821703158000,195825873726600,410720543218440,410720543218440,846739738410930,1772108740270440,1772108740270440,3647615648094990,7618942347630120,7618942347630120,15660031688889048,32650847564232672

%N a(n) is the maximal number of shortest knight's move paths, from origin at center of an infinite open chessboard, to square with coordinates <= n.

%C For n > 5 the distinct terms of this sequence are conjectured to be identical to A242512: precisely, A242514(n) = A242512(ceiling(2*(n+1)/3)).

%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=7, there are 240 shortest paths of length 6 steps from (0,0) to (7,7);

%e no square within 0 <= x,y <= 7 has more shortest paths.

%Y Cf. A242511, A242512, A242513, A183043, A242591.

%K easy,nonn,walk

%O 0,2

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