

A242591


Triangle of number of shortest knight paths T(n,k) from square (0,0) at center of an infinite open chessboard to square (n,k), for 0<=k<=n<=19.


6



1, 12, 2, 2, 1, 54, 6, 2, 9, 2, 2, 6, 1, 3, 32, 6, 28, 6, 24, 3, 8, 24, 3, 18, 1, 12, 85, 6, 100, 16, 95, 12, 60, 4, 25, 240, 6, 70, 4, 50, 1, 30, 201, 10, 60, 40, 330, 35, 266, 20, 150, 5, 66, 588, 20, 210, 10, 180, 5, 120, 1, 60, 462, 15, 147
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OFFSET

0,2


REFERENCES

Fred Lunnon, Knights in Daze, to appear.


LINKS

Georg Fischer, Table of n, a(n) for n = 0..209
Fred Lunnon, Revised tables & functions for knight's path distance and count (MAGMA code)


EXAMPLE

Triangle starts:
1,
12,2,
2,1,54,
6,2,9,2,
2,6,1,3,32,
6,28,6,24,3,8,
24,3,18,1,12,85,6,
100,16,95,12,60,4,25,240,
6,70,4,50,1,30,201,10,60,
40,330,35,266,20,150,5,66,588,20,
...
See examples under A242511.


PROG

(Magma) see attached afile for recursive & explicit algorithms


CROSSREFS

Cf. A242511, A242512, A242513, A242514, A183043.
Sequence in context: A010204 A124607 A177429 * A010205 A328844 A080496
Adjacent sequences: A242588 A242589 A242590 * A242592 A242593 A242594


KEYWORD

easy,nonn,walk,tabl


AUTHOR

Fred Lunnon, May 18 2014


EXTENSIONS

a(65) ff. exported to bfile by Georg Fischer, Jul 16 2020


STATUS

approved



