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A224310 T(n,k)=Number of nXk 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224310 #6 Jul 23 2025 05:05:42
%S A224310 3,9,9,22,54,27,46,218,324,81,86,698,1586,1944,243,148,1915,5996,
%T A224310 11361,11664,729,239,4690,20214,45453,82700,69984,2187,367,10511,
%U A224310 61953,164514,345875,615481,419904,6561,541,21919,174378,562760,1258372,2717759
%N A224310 T(n,k)=Number of nXk 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224310 Table starts
%C A224310 .....3........9.........22..........46..........86..........148..........239
%C A224310 .....9.......54........218.........698........1915.........4690........10511
%C A224310 ....27......324.......1586........5996.......20214........61953.......174378
%C A224310 ....81.....1944......11361.......45453......164514.......562760......1825800
%C A224310 ...243....11664......82700......345875.....1258372......4420701.....15312504
%C A224310 ...729....69984.....615481.....2717759.....9829605.....33934344....118317987
%C A224310 ..2187...419904....4634768....22071219....80083648....268379906....911404794
%C A224310 ..6561..2519424...35003328...182843194...677557164...2215451575...7236130163
%C A224310 .19683.15116544..264487714..1528645389..5882182248..19023816444..59751261572
%C A224310 .59049.90699264.1997888432.12825738594.51821072499.168305254414.512310103541
%H A224310 R. H. Hardin, <a href="/A224310/b224310.txt">Table of n, a(n) for n = 1..337</a>
%F A224310 Empirical for column k:
%F A224310 k=1: a(n) = 3*a(n-1)
%F A224310 k=2: a(n) = 6*a(n-1)
%F A224310 k=3: [order 17]
%F A224310 k=4: [order 30] for n>35
%F A224310 k=5: [order 61] for n>69
%F A224310 k=6: [order 88] for n>98
%F A224310 Empirical: rows n=1..7 are polynomials of degree 4*n for k>0,0,3,6,9,12,15
%e A224310 Some solutions for n=3 k=4
%e A224310 ..0..0..1..0....0..0..0..1....0..0..0..1....0..2..1..0....0..0..2..0
%e A224310 ..1..2..1..0....0..1..1..0....0..0..1..0....2..1..1..0....2..2..2..0
%e A224310 ..2..1..1..1....1..2..2..2....2..2..0..0....1..1..2..0....2..2..1..0
%Y A224310 Column 1 is A000244
%Y A224310 Column 2 is 9*6^(n-1)
%Y A224310 Row 1 is A223718
%Y A224310 Row 2 is A223927
%K A224310 nonn,tabl
%O A224310 1,1
%A A224310 _R. H. Hardin_ Apr 03 2013