A223864 - OEIS

%I #4 Mar 28 2013 07:23:29

%S 4,16,10,50,100,20,130,684,400,35,296,3526,4884,1225,56,610,14751,

%T 41682,24199,3136,84,1163,52591,273959,315124,93731,7056,120,2083,

%U 165212,1477240,3017129,1771012,303560,14400,165,3544,468292,6818350,22852913

%N T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing

%C Table starts

%C ...4....16.......50.......130.........296...........610...........1163

%C ..10...100......684......3526.......14751.........52591.........165212

%C ..20...400.....4884.....41682......273959.......1477240........6818350

%C ..35..1225....24199....315124.....3017129......22852913......144081276

%C ..56..3136....93731...1771012....23738426.....243933798.....2030417942

%C ..84..7056...303560...8008548...145947740....1989679315....21476594002

%C .120.14400...857696..30627033...740441932...13140481520...181330154458

%C .165.27225..2175884.102479569..3217594840...73068868012..1271807435844

%C .220.48400..5058530.307435001.12305144319..352040804450..7630189031428

%C .286.81796.10940664.842078930.42270004211.1502130487437.40055722078772

%H R. H. Hardin, <a href="/A223864/b223864.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,1,2,4,6

%F Empirical: rows n=1..7 are polynomials of degree 6*n

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000292(n+1)

%Y Column 2 is A001249

%Y Row 1 is A223659

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 28 2013