cp's OEIS Frontend

A184129 T(n,k)=Number of nXk 0..3 arrays with rows and columns in nondecreasing order.

%I A184129 #7 Jul 22 2025 09:27:31
%S A184129 4,10,10,20,86,20,35,561,561,35,56,2861,14178,2861,56,84,12068,276427,
%T A184129 276427,12068,84,120,43947,4249486,21907055,4249486,43947,120,165,
%U A184129 142376,53817407,1361812470,1361812470,53817407,142376,165,220,419213,581588614
%N A184129 T(n,k)=Number of nXk 0..3 arrays with rows and columns in nondecreasing order.
%C A184129 Empirical: T(n,k) for elements in 0..z is a polynomial in n of degree ((z+1)^k)-1 for fixed k
%C A184129 Table starts
%C A184129 ...4......10...........20................35......................56
%C A184129 ..10......86..........561..............2861...................12068
%C A184129 ..20.....561........14178............276427.................4249486
%C A184129 ..35....2861.......276427..........21907055..............1361812470
%C A184129 ..56...12068......4249486........1361812470............348053502590
%C A184129 ..84...43947.....53817407.......68564445616..........71759424776253
%C A184129 .120..142376....581588614.....2895890669208.......12323643023399737
%C A184129 .165..419213...5503143135...105444472863183.....1812407940171867666
%C A184129 .220.1139569..46473256070..3378291908588468...233154749874813919293
%C A184129 .286.2894178.355407459056.96731087997530019.26665385106037737856103
%H A184129 R. H. Hardin, <a href="/A184129/b184129.txt">Table of n, a(n) for n = 1..127</a>
%e A184129 Some solutions for 4X3
%e A184129 ..0..0..2....0..0..3....0..2..2....0..0..3....0..0..3....0..0..2....0..0..2
%e A184129 ..0..3..2....0..1..1....1..1..3....0..1..0....0..3..2....1..2..2....0..3..3
%e A184129 ..1..0..3....1..3..1....3..0..1....0..1..3....3..0..3....2..2..1....2..1..2
%e A184129 ..3..0..0....1..3..3....3..0..3....2..0..0....3..2..0....3..0..3....2..3..0
%Y A184129 Column 1 is A000292(n+1)
%Y A184129 Diagonal is A162086
%K A184129 nonn,tabl
%O A184129 1,1
%A A184129 _R. H. Hardin_ Jan 09 2011