%I #6 Nov 10 2015 12:23:30
%S 8,48,59,204,2282,360,770,54924,78306,2196,2687,1111442,8349744,
%T 2785493,13704,8559,20380008,830632993,1425379543,101776538,85189,
%U 25383,337841109,77648070968,714115802545,255768846517,3683279274,528559,71498
%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 filled by rows with each element moved a city block distance of 0 1 or 2, and rows and columns in increasing lexicographic order.
%C Table starts
%C .......8...........48............204.............770............2687
%C ......59.........2282..........54924.........1111442........20380008
%C .....360........78306........8349744.......830632993.....77648070968
%C ....2196......2785493.....1425379543....714115802545.337720306039004
%C ...13704....101776538...255768846517.646202010775260
%C ...85189...3683279274.45106218220800
%C ..528559.133026960133
%C .3280284
%H R. H. Hardin, <a href="/A263506/b263506.txt">Table of n, a(n) for n = 1..40</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 15]
%F Empirical for row n:
%F n=1: [linear recurrence of order 13]
%e Some solutions for n=2 k=4
%e ..0..1..2..4.14....0..3..6..7..8....0..1..2..3..4....0..1..2..4.14
%e ..5..7.13..9..3....5.11..9..2.14....5..8..9..7.13....5.12.11..9..3
%e .10.12..6.11..8...10..1.13.12..4...10..6.11.14.12...10..6..7.13..8
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 19 2015