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A223864 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223864 #6 Jul 23 2025 04:36:15
%S A223864 4,16,10,50,100,20,130,684,400,35,296,3526,4884,1225,56,610,14751,
%T A223864 41682,24199,3136,84,1163,52591,273959,315124,93731,7056,120,2083,
%U A223864 165212,1477240,3017129,1771012,303560,14400,165,3544,468292,6818350,22852913
%N A223864 T(n,k)=Number of nXk 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223864 Table starts
%C A223864 ...4....16.......50.......130.........296...........610...........1163
%C A223864 ..10...100......684......3526.......14751.........52591.........165212
%C A223864 ..20...400.....4884.....41682......273959.......1477240........6818350
%C A223864 ..35..1225....24199....315124.....3017129......22852913......144081276
%C A223864 ..56..3136....93731...1771012....23738426.....243933798.....2030417942
%C A223864 ..84..7056...303560...8008548...145947740....1989679315....21476594002
%C A223864 .120.14400...857696..30627033...740441932...13140481520...181330154458
%C A223864 .165.27225..2175884.102479569..3217594840...73068868012..1271807435844
%C A223864 .220.48400..5058530.307435001.12305144319..352040804450..7630189031428
%C A223864 .286.81796.10940664.842078930.42270004211.1502130487437.40055722078772
%H A223864 R. H. Hardin, <a href="/A223864/b223864.txt">Table of n, a(n) for n = 1..312</a>
%F A223864 Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,1,2,4,6
%F A223864 Empirical: rows n=1..7 are polynomials of degree 6*n
%e A223864 Some solutions for n=3 k=4
%e A223864 ..0..0..0..0....0..2..1..1....0..1..3..2....0..2..2..0....0..1..1..3
%e A223864 ..0..0..0..1....0..2..3..1....0..2..3..2....1..3..3..2....0..1..3..3
%e A223864 ..2..3..2..2....0..2..3..3....1..3..3..3....3..3..3..2....1..3..3..3
%Y A223864 Column 1 is A000292(n+1)
%Y A223864 Column 2 is A001249
%Y A223864 Row 1 is A223659
%K A223864 nonn,tabl
%O A223864 1,1
%A A223864 _R. H. Hardin_ Mar 28 2013