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T(n,k)=Number of nXk array permutations with each element making zero or one knight moves
6

%I #5 Mar 31 2012 12:36:14

%S 1,1,1,1,1,1,1,4,4,1,1,16,49,16,1,1,36,569,569,36,1,1,81,4372,22865,

%T 4372,81,1,1,225,42689,602565,602565,42689,225,1,1,625,412189,

%U 20037184,46350185,20037184,412189,625,1,1,1600,3988132,697391125,5025299720

%N T(n,k)=Number of nXk array permutations with each element making zero or one knight moves

%C Table starts

%C .1....1.......1.........1..........1..........1............1...........1

%C .1....1.......4........16.........36.........81..........225.........625

%C .1....4......49.......569.......4372......42689.......412189.....3988132

%C .1...16.....569.....22865.....602565...20037184....697391125.23675552985

%C .1...36....4372....602565...46350185.5025299720.585494657168

%C .1...81...42689..20037184.5025299720

%C .1..225..412189.697391125

%C .1..625.3988132

%C .1.1600

%C .1

%H R. H. Hardin, <a href="/A189150/b189150.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for 5X3

%e ..5..8..2....0..8..3....5..8..7....7..8..2....0..8..2....7..1..2....5..6..7

%e ..3..4..0....2..9.10....2..4.10...10..4..5....3.11.10...10.11..0....3..4..0

%e ..1.12.13....1..7.13....6..0..1...13..0..1...13..7..1....5.14..8....1..2..8

%e .14.10.11....4..5.11...14..3.12...14..3.12....9..5..4....4..3..6....9.10.12

%e ..7..6..9...12..6.14...11.13..9...11..6..9...12..6.14...12.13..9...11.13.14

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_ Apr 17 2011