A201101 T(n,k)=Number of nXk 0..7 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

8, 28, 28, 56, 140, 56, 70, 140, 140, 70, 56, 14, 252, 14, 56, 28, 728, 10423, 10423, 728, 28, 8, 3696, 6972, 2490, 6972, 3696, 8, 1, 3273, 85005, 905695, 905695, 85005, 3273, 1, 8, 323, 478198, 89311, 1445712, 89311, 478198, 323, 8, 28, 10516, 27782, 31885648

Offset

1,1

Comments

Table starts

..8....28......56........70...........56.............28..............8

.28...140.....140........14..........728...........3696...........3273

.56...140.....252.....10423.........6972..........85005.........478198

.70....14...10423......2490.......905695..........89311.......31885648

.56...728....6972....905695......1445712.......55782998......945668958

.28..3696...85005.....89311.....55782998.....2244318652....12230511648

..8..3273..478198..31885648....945668958....12230511648....80495995176

..1...323...27782...2647438....123026475.....5732148226...155796077603

..8.10516.3937944.656371640..46355746304..1359373604245.18098348588856

.28.37590.5383954..36544193.138881000080.28620297165083

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

T(n,1) = binomial(8,n modulo 8). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

Example

Some solutions for n=3 k=3
..0..1..1....0..2..4....0..1..3....0..1..2....0..3..6....0..2..3....0..1..5
..2..4..5....1..3..6....2..5..7....0..4..5....1..4..7....1..4..6....2..3..6
..3..6..7....1..5..7....4..6..7....3..6..7....2..5..7....2..5..7....4..4..7

Crossrefs

Sequence in context: A272259 A112663 A220288 * A201105 A184614 A006377

Adjacent sequences: A201098 A201099 A201100 * A201102 A201103 A201104

Keyword

nonn,tabl

Author

R. H. Hardin Nov 26 2011

Status

approved