A242591 - OEIS

%I #24 Jan 03 2025 18:22:29

%S 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,

%T 16,95,12,60,4,25,240,6,70,4,50,1,30,201,10,60,40,330,35,266,20,150,5,

%U 66,588,20,210,10,180,5,120,1,60,462,15,147,1512

%N 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.

%H Georg Fischer, <a href="/A242591/b242591.txt">Table of n, a(n) for n = 0..209</a>

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

%e Triangle starts:

%e     1;

%e    12,   2;

%e     2,   1, 54;

%e     6,   2,  9,   2;

%e     2,   6,  1,   3, 32;

%e     6,  28,  6,  24,  3,   8;

%e    24,   3, 18,   1, 12,  85,   6;

%e   100,  16, 95,  12, 60,   4,  25, 240;

%e     6,  70,  4,  50,  1,  30, 201,  10,  60;

%e    40, 330, 35, 266, 20, 150,   5,  66, 588, 20;

%e   ...

%e See examples under A242511.

%o (Magma) // See attached a-file for recursive & explicit algorithms.

%Y Cf. A242511, A242512, A242513, A242514, A183043.

%K easy,nonn,walk,tabl

%O 0,2

%A _Fred Lunnon_, May 18 2014

%E a(66) ff. exported to b-file by _Georg Fischer_, Jul 16 2020