Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Mar 31 2012 12:35:56
%S 4,10,10,20,86,20,35,561,561,35,56,2861,14178,2861,56,84,12068,276427,
%T 276427,12068,84,120,43947,4249486,21907055,4249486,43947,120,165,
%U 142376,53817407,1361812470,1361812470,53817407,142376,165,220,419213,581588614
%N T(n,k)=Number of nXk 0..3 arrays with rows and columns in nondecreasing order
%C Empirical: T(n,k) for elements in 0..z is a polynomial in n of degree ((z+1)^k)-1 for fixed k
%C Table starts
%C ...4......10...........20................35......................56
%C ..10......86..........561..............2861...................12068
%C ..20.....561........14178............276427.................4249486
%C ..35....2861.......276427..........21907055..............1361812470
%C ..56...12068......4249486........1361812470............348053502590
%C ..84...43947.....53817407.......68564445616..........71759424776253
%C .120..142376....581588614.....2895890669208.......12323643023399737
%C .165..419213...5503143135...105444472863183.....1812407940171867666
%C .220.1139569..46473256070..3378291908588468...233154749874813919293
%C .286.2894178.355407459056.96731087997530019.26665385106037737856103
%H R. H. Hardin, <a href="/A184129/b184129.txt">Table of n, a(n) for n = 1..127</a>
%e Some solutions for 4X3
%e ..0..0..2....0..0..3....0..2..2....0..0..3....0..0..3....0..0..2....0..0..2
%e ..0..3..2....0..1..1....1..1..3....0..1..0....0..3..2....1..2..2....0..3..3
%e ..1..0..3....1..3..1....3..0..1....0..1..3....3..0..3....2..2..1....2..1..2
%e ..3..0..0....1..3..3....3..0..3....2..0..0....3..2..0....3..0..3....2..3..0
%Y Column 1 is A000292(n+1)
%Y Diagonal is A162086
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 09 2011