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A224204 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224204 #6 Jul 23 2025 05:03:11
%S A224204 4,16,16,50,160,64,130,984,1600,256,296,4580,16060,16000,1024,610,
%T A224204 17723,108625,263516,160000,4096,1163,59792,586343,2411246,4357084,
%U A224204 1600000,16384,2083,180821,2734683,16355242,54177872,72105068,16000000,65536
%N A224204 T(n,k)=Number of nXk 0..3 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224204 Table starts
%C A224204 .......4..........16............50.............130..............296
%C A224204 ......16.........160...........984............4580............17723
%C A224204 ......64........1600.........16060..........108625...........586343
%C A224204 .....256.......16000........263516.........2411246.........16355242
%C A224204 ....1024......160000.......4357084........54177872........451319098
%C A224204 ....4096.....1600000......72105068......1229044416......12652618110
%C A224204 ...16384....16000000....1193130640.....27957232796.....357890479324
%C A224204 ...65536...160000000...19742052632....636184842092...10153767871028
%C A224204 ..262144..1600000000..326659600368..14476260508500..288290902851198
%C A224204 .1048576.16000000000.5405039750704.329391607167600.8186391229197618
%H A224204 R. H. Hardin, <a href="/A224204/b224204.txt">Table of n, a(n) for n = 1..511</a>
%F A224204 Empirical: columns k=1..7 have recurrences of order 1,1,7,10,19,25,41 for n>0,0,0,12,23,32,48
%F A224204 Empirical: rows n=1..7 are polynomials of degree 6*n for k>0,0,0,2,3,4,5
%e A224204 Some solutions for n=3 k=4
%e A224204 ..0..0..1..1....0..1..2..1....1..1..0..0....2..1..1..0....0..1..2..2
%e A224204 ..1..1..2..0....3..2..2..0....2..3..3..3....1..3..3..0....1..3..3..3
%e A224204 ..1..2..3..3....3..3..3..1....3..3..3..0....3..3..2..1....3..3..3..1
%Y A224204 Column 1 is A000302
%Y A224204 Column 2 is 16*10^(n-1)
%Y A224204 Row 1 is A223659
%Y A224204 Row 2 is A224058
%K A224204 nonn,tabl
%O A224204 1,1
%A A224204 _R. H. Hardin_ Apr 01 2013