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A223975 T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal.

%I A223975 #6 Jul 23 2025 04:44:15
%S A223975 3,9,9,22,81,27,46,484,729,81,86,2116,9515,6561,243,148,7396,76092,
%T A223975 186004,59049,729,239,21904,440628,2558848,3628696,531441,2187,367,
%U A223975 57121,2026448,22935921,84988435,70779056,4782969,6561,541,134689,7829639
%N A223975 T(n,k)=Number of nXk 0..2 arrays with rows and antidiagonals unimodal.
%C A223975 Table starts
%C A223975 .....3..........9.............22...............46.................86
%C A223975 .....9.........81............484.............2116...............7396
%C A223975 ....27........729...........9515............76092.............440628
%C A223975 ....81.......6561.........186004..........2558848...........22935921
%C A223975 ...243......59049........3628696.........84988435.........1140963027
%C A223975 ...729.....531441.......70779056.......2809740785........55803232969
%C A223975 ..2187....4782969.....1380511272......92756321858......2708281019793
%C A223975 ..6561...43046721....26926081924....3060966419662....131014406127439
%C A223975 .19683..387420489...525177301935..100999995564503...6329626912147424
%C A223975 .59049.3486784401.10243271456697.3332485315028073.305632588672082728
%H A223975 R. H. Hardin, <a href="/A223975/b223975.txt">Table of n, a(n) for n = 1..286</a>
%F A223975 Empirical: columns k=1..6 have recurrences of order 1,1,7,18,43,91
%F A223975 Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,0,0,2,3,4
%e A223975 Some solutions for n=3 k=4
%e A223975 ..0..2..0..0....1..2..2..1....2..1..1..0....1..2..2..0....0..0..0..0
%e A223975 ..0..1..2..1....0..0..1..1....1..2..2..2....0..2..1..0....0..2..2..0
%e A223975 ..0..1..2..2....0..1..0..0....0..1..1..2....1..1..0..0....0..2..1..1
%Y A223975 Column 1 is A000244
%Y A223975 Column 2 is A001019
%Y A223975 Row 1 is A223718
%Y A223975 Row 2 is A223719
%K A223975 nonn,tabl
%O A223975 1,1
%A A223975 _R. H. Hardin_ Mar 30 2013