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A224281 T(n,k)=Number of nXk 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224281 #6 Jul 23 2025 05:04:26
%S A224281 4,16,16,50,160,64,130,984,1600,256,296,4580,13683,16000,1024,610,
%T A224281 17723,84132,186516,160000,4096,1163,59792,442089,1334973,2596992,
%U A224281 1600000,16384,2083,180821,2059793,8073038,21348990,37128051,16000000,65536,3544
%N A224281 T(n,k)=Number of nXk 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224281 Table starts
%C A224281 .......4..........16............50............130.............296
%C A224281 ......16.........160...........984...........4580...........17723
%C A224281 ......64........1600.........13683..........84132..........442089
%C A224281 .....256.......16000........186516........1334973.........8073038
%C A224281 ....1024......160000.......2596992.......21348990.......137489538
%C A224281 ....4096.....1600000......37128051......356222482......2425304290
%C A224281 ...16384....16000000.....537465766.....6172817040.....45275725025
%C A224281 ...65536...160000000....7804602744...109166159263....883012703273
%C A224281 ..262144..1600000000..113382138975..1947747629183..17667432461262
%C A224281 .1048576.16000000000.1646661944858.34864494529806.358042017265316
%H A224281 R. H. Hardin, <a href="/A224281/b224281.txt">Table of n, a(n) for n = 1..199</a>
%F A224281 Empirical: columns k=1..4 have recurrences of order 1,1,25,52 for n>0,0,26,59
%F A224281 Empirical: rows n=1..6 are polynomials of degree 6*n for k>0,0,3,7,11,15
%e A224281 Some solutions for n=3 k=4
%e A224281 ..0..2..2..1....3..0..0..0....0..0..3..2....3..2..1..1....0..1..1..1
%e A224281 ..2..2..2..0....1..2..3..0....3..3..2..0....3..2..2..2....1..2..3..0
%e A224281 ..3..2..2..1....3..3..2..2....3..3..3..2....2..3..2..2....3..3..0..0
%Y A224281 Column 1 is A000302
%Y A224281 Column 2 is 16*10^(n-1)
%Y A224281 Row 1 is A223659
%Y A224281 Row 2 is A224058
%K A224281 nonn,tabl
%O A224281 1,1
%A A224281 _R. H. Hardin_ Apr 02 2013