A242514 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.

1, 12, 54, 54, 54, 54, 85, 240, 240, 588, 1512, 1512, 3564, 8700, 8700, 19965, 47124, 47124, 105963, 244244, 244244, 540540, 1224080, 1224080, 2674984, 5974956, 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

Offset

0,2

Comments

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)).

References

Fred Lunnon, Knights in Daze, to appear.

Links

Table of n, a(n) for n=0..70.

Fred Lunnon, Revised tables & functions for knight's path distance and count (MAGMA code)

Example

For n=7, there are 240 shortest paths of length 6 steps from (0,0) to (7,7);
no square within 0 <= x,y <= 7 has more shortest paths.

Crossrefs

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

Sequence in context: A253130 A213549 A211060 * A030182 A060171 A133078

Adjacent sequences: A242511 A242512 A242513 * A242515 A242516 A242517

Keyword

easy,nonn,walk

Author

Fred Lunnon, May 16 2014 and May 18 2014

Status

approved