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A263586 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 1 or 2, and rows and columns in increasing lexicographic order. 9

%I

%S 1,6,4,12,134,18,31,1992,3035,70,89,27650,145151,69084,292,230,343431,

%T 8296414,14088801,1643235,1212,536,3777963,479355276,3822509358,

%U 1544467524,38562523,5028,1171,38762619,24453863816,1035523589834

%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 1 or 2, and rows and columns in increasing lexicographic order.

%C Table starts

%C .....1.........6...........12............31............89.............230

%C .....4.......134.........1992.........27650........343431.........3777963

%C ....18......3035.......145151.......8296414.....479355276.....24453863816

%C ....70.....69084.....14088801....3822509358.1035523589834.244734723702847

%C ...292...1643235...1544467524.1954083613268

%C ..1212..38562523.162168224979

%C ..5028.903637375

%C .20832

%H R. H. Hardin, <a href="/A263586/b263586.txt">Table of n, a(n) for n = 1..40</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) +2*a(n-3) +4*a(n-4) -8*a(n-5)

%F k=2: [order 84]

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) -2*a(n-5) +3*a(n-6) -a(n-8) for n>9

%e Some solutions for n=3 k=4

%e ..1..3..4..7..9....1..5..7..9.14....1..3..4..7..9....1..5..7..8..9

%e ..6..0..5..2..8....6..0..2.12..4....6..0..5..2..8....6..0.12.13..3

%e .11.15.10.19.12...11.15..8..3.13...11.15.10.19.18...11.15..2.14..4

%e .16.17.18.13.14...17.10.16.19.18...17.12.16.13.14...17.10.19.16.18

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 22 2015

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Last modified January 28 14:10 EST 2023. Contains 359895 sequences. (Running on oeis4.)