|
|
A202756
|
|
T(n,k)=Number of nXk nonnegative integer arrays with each row and column increasing from zero by 0 or 1
|
|
6
|
|
|
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, 184, 184, 51, 7, 1, 1, 8, 78, 462, 924, 462, 78, 8, 1, 1, 9, 113, 1022, 3809, 3809, 1022, 113, 9, 1, 1, 10, 157, 2052, 13197, 26394, 13197, 2052, 157, 10, 1, 1, 11, 211, 3819, 39675
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
Table starts
.1..1...1....1......1........1.........1...........1............1
.1..2...3....4......5........6.........7...........8............9
.1..3...8...17.....31.......51........78.........113..........157
.1..4..17...62....184......462......1022........2052.........3819
.1..5..31..184....924.....3809.....13197.......39675.......106357
.1..6..51..462...3809....26394....150777......721382......2964632
.1..7..78.1022..13197...150777...1442764....11408125.....75393424
.1..8.113.2052..39675...721382..11408125...150786848...1649287336
.1..9.157.3819.106357..2964632..75393424..1649287336..30114993376
.1.10.211.6688.259669.10720688.424992394.15057496688.455474662471
|
|
LINKS
|
|
|
FORMULA
|
Empirical: Columns of T(n,k) are a polynomial in n of degree k*(k-1)/2.
For elements increasing by 0..d instead of 0..1, columns are a polynomial of degree d*k*(k-1)/2.
|
|
EXAMPLE
|
Some solutions for n=5 k=3
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..0..0....0..0..1....0..0..0....0..1..1....0..1..1....0..0..0....0..0..0
..0..0..1....0..0..1....0..0..0....0..1..1....0..1..2....0..0..0....0..0..0
..0..0..1....0..1..1....0..0..1....0..1..2....0..1..2....0..0..0....0..0..0
..0..0..1....0..1..2....0..1..1....0..1..2....0..1..2....0..1..1....0..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|