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A263506 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. 7

%I

%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

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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)