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%I #6 Nov 10 2015 12:19:46
%S 2,7,8,15,144,24,27,1687,1962,60,55,13455,69792,24091,160,109,105222,
%T 1880912,2736666,317857,448,199,747253,51961032,248766606,123176874,
%U 4177099,1232,347,4989566,1372902790,25103852988,40226420700,5641347668
%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 or 2, and rows and columns in increasing lexicographic order.
%C Table starts
%C ....2.........7...........15............27.............55...........109
%C ....8.......144.........1687.........13455.........105222........747253
%C ...24......1962........69792.......1880912.......51961032....1372902790
%C ...60.....24091......2736666.....248766606....25103852988.2343241421547
%C ..160....317857....123176874...40226420700.14573046651208
%C ..448...4177099...5641347668.6430889476830
%C .1232..54493144.249947653938
%C .3344.712019936
%C .9120
%H R. H. Hardin, <a href="/A263602/b263602.txt">Table of n, a(n) for n = 1..49</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +4*a(n-3) +4*a(n-4)
%F k=2: [order 53]
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) -3*a(n-2) +2*a(n-3) -a(n-4) -a(n-5) +a(n-6) for n>8
%F n=2: [order 73] for n>77
%e Some solutions for n=3 k=4
%e ..0..1..2..3..4....0..1..2..7.14....0..1..2..3.14....0..1..2..3..4
%e ..5..6.11.18..9....5.12.13.18..3....5.12.11..6..9....5.12.17..6..9
%e .10..7.16.19..8...10.17..6.19..4...10..7.16.19..4...10.13.18..7..8
%e .15.12.13.14.17...15.16.11..8..9...15.18.17..8.13...15.16.11.14.19
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Oct 22 2015
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