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T(n,k)=Number of nXk 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope
4

%I #4 Mar 14 2013 06:50:35

%S 4,16,16,64,150,64,256,1080,1080,256,1024,6627,38512,6627,1024,4096,

%T 36552,899390,899390,36552,4096,16384,187000,22520656,59844888,

%U 22520656,187000,16384,65536,905440,462313688,4842450790,4842450790,462313688

%N T(n,k)=Number of nXk 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope

%C Table starts

%C ......4......16.........64..........256..........1024.........4096

%C .....16.....150.......1080.........6627.........36552.......187000

%C .....64....1080......38512.......899390......22520656....462313688

%C ....256....6627.....899390.....59844888....4842450790.268351320214

%C ...1024...36552...22520656...4842450790.1962060592992

%C ...4096..187000..462313688.268351320214

%C ..16384..905440.9567328752

%C ..65536.4206453

%C .262144

%H R. H. Hardin, <a href="/A223071/b223071.txt">Table of n, a(n) for n = 1..49</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000302

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 14 2013