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A224012 T(n,k)=Number of nXk 0..2 arrays with rows nondecreasing and antidiagonals unimodal.

%I A224012 #6 Jul 23 2025 04:51:25
%S A224012 3,6,9,10,36,27,15,100,216,81,21,225,868,1296,243,28,441,2661,7378,
%T A224012 7776,729,36,784,6815,28541,62764,46656,2187,45,1296,15340,90051,
%U A224012 297859,534352,279936,6561,55,2025,31324,245055,1108969,3094127,4549684,1679616
%N A224012 T(n,k)=Number of nXk 0..2 arrays with rows nondecreasing and antidiagonals unimodal.
%C A224012 Table starts
%C A224012 .....3........6.........10..........15...........21............28............36
%C A224012 .....9.......36........100.........225..........441...........784..........1296
%C A224012 ....27......216........868........2661.........6815.........15340.........31324
%C A224012 ....81.....1296.......7378.......28541........90051........245055........595822
%C A224012 ...243.....7776......62764......297859......1108969.......3516324.......9866389
%C A224012 ...729....46656.....534352.....3094127.....13275381......47735665.....150787422
%C A224012 ..2187...279936....4549684....32148473....157347899.....630339756....2200064042
%C A224012 ..6561..1679616...38737252...334179881...1859567103....8213689391...31256208954
%C A224012 .19683.10077696..329817976..3474343713..21962353421..106375878027..437370837827
%C A224012 .59049.60466176.2808146488.36122604265.259365424097.1373916879120.6067995150599
%H A224012 R. H. Hardin, <a href="/A224012/b224012.txt">Table of n, a(n) for n = 1..449</a>
%F A224012 Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19
%F A224012 Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,1,2,3,4,5
%e A224012 Some solutions for n=3 k=4
%e A224012 ..1..1..2..2....0..1..1..1....0..0..0..0....0..0..0..1....0..2..2..2
%e A224012 ..0..2..2..2....0..1..1..1....0..1..2..2....2..2..2..2....0..0..1..1
%e A224012 ..1..1..2..2....0..2..2..2....1..2..2..2....2..2..2..2....0..0..2..2
%Y A224012 Column 1 is A000244
%Y A224012 Column 2 is A000400
%Y A224012 Row 1 is A000217(n+1)
%Y A224012 Row 2 is A000537(n+1)
%K A224012 nonn,tabl
%O A224012 1,1
%A A224012 _R. H. Hardin_ Mar 30 2013