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T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nXk array
6

%I #4 Dec 25 2012 08:57:40

%S 4,4,4,10,13,10,20,41,41,20,35,114,283,114,35,56,260,1448,1448,260,56,

%T 84,545,6687,15360,6687,545,84,120,1104,29847,149336,149336,29847,

%U 1104,120,165,2182,128985,1346477,2960327,1346477,128985,2182,165,220,4201,528548

%N T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nXk array

%C Table starts

%C ...4.....4......10........20..........35..........56..........84...........120

%C ...4....13......41.......114.........260.........545........1104..........2182

%C ..10....41.....283......1448........6687.......29847......128985........528548

%C ..20...114....1448.....15360......149336.....1346477....11432523......90627413

%C ..35...260....6687....149336.....2960327....52591889...861894138...13241462045

%C ..56...545...29847...1346477....52591889..1794793653.55877166390.1645212608113

%C ..84..1104..128985..11432523...861894138.55877166390

%C .120..2182..528548..90627413.13241462045

%C .165..4201.2040761.672437960

%C .220..7862.7473305

%C .286.14295

%C .364

%H R. H. Hardin, <a href="/A220931/b220931.txt">Table of n, a(n) for n = 1..84</a>

%e Some solutions for n=3 k=4

%e ..0..0..0..2....0..0..0..1....0..0..2..1....0..0..2..2....1..1..1..3

%e ..0..0..2..2....0..0..1..3....0..1..0..0....0..0..1..3....1..1..1..3

%e ..2..2..3..3....0..0..3..3....1..0..0..0....0..1..1..3....1..1..2..3

%Y Column 1 is A000292 for n>1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 25 2012