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A224190 T(n,k) = Number of n X k 0..2 arrays with rows unimodal and columns nondecreasing.

%I A224190 #6 Jan 15 2022 23:10:09
%S A224190 3,9,6,22,36,10,46,158,100,15,86,548,684,225,21,148,1600,3526,2205,
%T A224190 441,28,239,4102,14751,15779,5852,784,36,367,9503,52591,89380,55438,
%U A224190 13524,1296,45,541,20299,165212,422488,408222,163746,28176,2025,55,771,40570
%N A224190 T(n,k) = Number of n X k 0..2 arrays with rows unimodal and columns nondecreasing.
%C A224190 Table starts
%C A224190 ..3....9.....22......46.......86........148.........239..........367
%C A224190 ..6...36....158.....548.....1600.......4102........9503........20299
%C A224190 .10..100....684....3526....14751......52591......165212.......468292
%C A224190 .15..225...2205...15779....89380.....422488.....1727738......6272940
%C A224190 .21..441...5852...55438...408222....2469182....12741432.....57644194
%C A224190 .28..784..13524..163746..1519738...11444292....72710554....400958714
%C A224190 .36.1296..28176..424326..4844576...44435746...340780382...2249643632
%C A224190 .45.2025..54153..992607.13669953..150015321..1366188661..10635858679
%C A224190 .55.3025..97570.2138488.34953776..452158538..4823267213..43724068755
%C A224190 .66.4356.166738.4305730.82399174.1240740774.15322738603.159999462711
%H A224190 R. H. Hardin, <a href="/A224190/b224190.txt">Table of n, a(n) for n = 1..722</a>
%F A224190 Empirical: columns k=1..7 are polynomials of degree 2*k.
%F A224190 Empirical: rows n=1..7 are polynomials of degree 4*n.
%e A224190 Some solutions for n=3, k=4
%e A224190 ..1..2..2..1....0..0..2..0....1..2..1..1....0..1..0..0....1..0..0..0
%e A224190 ..1..2..2..1....1..2..2..0....1..2..1..1....0..1..2..0....1..1..0..0
%e A224190 ..2..2..2..2....1..2..2..1....2..2..1..1....0..2..2..0....1..1..0..0
%Y A224190 Column 1 is A000217(n+1).
%Y A224190 Column 2 is A000537(n+1).
%Y A224190 Row 1 is A223718.
%Y A224190 Row 2 is A223919.
%Y A224190 Row 3 is A223865.
%K A224190 nonn,tabl
%O A224190 1,1
%A A224190 _R. H. Hardin_ Apr 01 2013