A242513 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.

1, 1, 2, 12, 54, 100, 330, 1050, 3024, 8736, 23220, 62700, 158004, 406692, 986986, 2452450, 5788640, 14002560, 32357052, 76640148, 174174520, 405623400, 909582212, 2089064516, 4633556448, 10519464000, 23120533800, 51977741400, 113365499940, 252725219460, 547593359850, 1211884139250, 2610998927040, 5741708459520, 12309472580460, 26917328938500

Offset

0,3

Comments

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

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

References

Fred Lunnon, Knights in Daze, to appear.

Links

Table of n, a(n) for n=0..35.

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

Example

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.

Crossrefs

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

Sequence in context: A139046 A036359 A055703 * A006738 A212697 A111642

Adjacent sequences: A242510 A242511 A242512 * A242514 A242515 A242516

Keyword

easy,nonn,walk

Author

Fred Lunnon, May 16 2014 and May 18 2014

Status

approved