A202924 T(n,k)=Number of nXk nonnegative integer arrays with each row and column increasing from zero by 0, 1, 2 or 3

1, 1, 1, 1, 4, 1, 1, 10, 10, 1, 1, 20, 90, 20, 1, 1, 35, 534, 534, 35, 1, 1, 56, 2310, 11016, 2310, 56, 1, 1, 84, 8012, 150590, 150590, 8012, 84, 1, 1, 120, 23661, 1441046, 7083180, 1441046, 23661, 120, 1, 1, 165, 61830, 10457226, 220242352, 220242352, 10457226

Offset

1,5

Comments

Table starts

.1...1......1..........1.............1.................1.....................1

.1...4.....10.........20............35................56....................84

.1..10.....90........534..........2310..............8012.................23661

.1..20....534......11016........150590...........1441046..............10457226

.1..35...2310.....150590.......7083180.........220242352............4694959782

.1..56...8012....1441046.....220242352.......23491810780.........1652619440763

.1..84..23661...10457226....4694959782.....1652619440763.......398328574277322

.1.120..61830...61213311...73210175188....78726503296249.....63219027201690907

.1.165.146718..302092215..884548287930..2676714904101546...6740977636445383462

.1.220.321970.1297497783.8662839281016.68406213820923245.504159442506496670736

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical: columns of T(n,k) are polynomials in n of degree 3*k*(k-1)/2.

For elements increasing by 0..d instead of 0..3, 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..1..2....0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..2
..0..3..3....0..0..2....0..0..1....0..3..3....0..0..3....0..2..2....0..1..3
..0..3..3....0..1..3....0..1..2....0..3..3....0..2..3....0..2..5....0..3..3
..0..3..4....0..2..4....0..2..4....0..3..5....0..3..5....0..3..6....0..3..3

Crossrefs

Column 2 is A000292

Sequence in context: A089447 A082680 A056939 * A142595 A174669 A140711

Adjacent sequences: A202921 A202922 A202923 * A202925 A202926 A202927

Keyword

nonn,tabl

Author

R. H. Hardin Dec 26 2011

Status

approved