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A224374 T(n,k)=Number of nXk 0..2 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224374 #6 Jul 23 2025 05:07:49
%S A224374 3,9,9,22,54,27,46,218,324,81,86,698,1838,1944,243,148,1915,7608,
%T A224374 15540,11664,729,239,4690,26314,77793,132236,69984,2187,367,10511,
%U A224374 80819,311367,800309,1126072,419904,6561,541,21919,227112,1092281,3607078,8297747
%N A224374 T(n,k)=Number of nXk 0..2 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224374 Table starts
%C A224374 .....3........9.........22..........46...........86...........148
%C A224374 .....9.......54........218.........698.........1915..........4690
%C A224374 ....27......324.......1838........7608........26314.........80819
%C A224374 ....81.....1944......15540.......77793.......311367.......1092281
%C A224374 ...243....11664.....132236......800309......3607078......13831334
%C A224374 ...729....69984....1126072.....8297747.....42132769.....174854516
%C A224374 ..2187...419904....9588028....86251004....495660330....2231009824
%C A224374 ..6561..2519424...81634704...896856330...5848449149...28645726612
%C A224374 .19683.15116544..695055928..9325161494..69064897862..368818252942
%C A224374 .59049.90699264.5917866680.96954549463.815702088065.4752723627808
%H A224374 R. H. Hardin, <a href="/A224374/b224374.txt">Table of n, a(n) for n = 1..1008</a>
%F A224374 Empirical: columns k=1..7 have recurrences of order 1,1,5,7,11,14,19 for n>0,0,0,8,13,18,24
%F A224374 Empirical: rows n=1..7 are polynomials of order 4*n for k>0,0,0,2,3,4,5
%e A224374 Some solutions for n=3 k=4
%e A224374 ..2..2..2..2....0..0..1..2....1..2..0..0....1..2..1..1....1..1..2..0
%e A224374 ..2..2..2..1....2..2..2..2....2..1..1..1....2..2..2..2....1..2..2..0
%e A224374 ..2..2..2..1....2..2..2..2....2..2..1..1....2..2..2..0....2..2..1..1
%Y A224374 Column 1 is A000244
%Y A224374 Column 2 is 9*6^(n-1)
%Y A224374 Row 1 is A223718
%Y A224374 Row 2 is A223927
%K A224374 nonn,tabl
%O A224374 1,1
%A A224374 _R. H. Hardin_ Apr 05 2013