A202756 - OEIS

%I #5 Mar 31 2012 12:36:51

%S 1,1,1,1,2,1,1,3,3,1,1,4,8,4,1,1,5,17,17,5,1,1,6,31,62,31,6,1,1,7,51,

%T 184,184,51,7,1,1,8,78,462,924,462,78,8,1,1,9,113,1022,3809,3809,1022,

%U 113,9,1,1,10,157,2052,13197,26394,13197,2052,157,10,1,1,11,211,3819,39675

%N T(n,k)=Number of nXk nonnegative integer arrays with each row and column increasing from zero by 0 or 1

%C Table starts

%C .1..1...1....1......1........1.........1...........1............1

%C .1..2...3....4......5........6.........7...........8............9

%C .1..3...8...17.....31.......51........78.........113..........157

%C .1..4..17...62....184......462......1022........2052.........3819

%C .1..5..31..184....924.....3809.....13197.......39675.......106357

%C .1..6..51..462...3809....26394....150777......721382......2964632

%C .1..7..78.1022..13197...150777...1442764....11408125.....75393424

%C .1..8.113.2052..39675...721382..11408125...150786848...1649287336

%C .1..9.157.3819.106357..2964632..75393424..1649287336..30114993376

%C .1.10.211.6688.259669.10720688.424992394.15057496688.455474662471

%H R. H. Hardin, <a href="/A202756/b202756.txt">Table of n, a(n) for n = 1..684</a>

%F Empirical: Columns of T(n,k) are a polynomial in n of degree k*(k-1)/2.

%F For elements increasing by 0..d instead of 0..1, columns are a polynomial of degree d*k*(k-1)/2.

%e Some solutions for n=5 k=3

%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0

%e ..0..0..0....0..0..1....0..0..0....0..1..1....0..1..1....0..0..0....0..0..0

%e ..0..0..1....0..0..1....0..0..0....0..1..1....0..1..2....0..0..0....0..0..0

%e ..0..0..1....0..1..1....0..0..1....0..1..2....0..1..2....0..0..0....0..0..0

%e ..0..0..1....0..1..2....0..1..1....0..1..2....0..1..2....0..1..1....0..0..0

%Y Column 3 is A105163(n+1)

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Dec 23 2011