A201072 T(n,k)=Number of nXk 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

7, 21, 21, 35, 70, 35, 35, 35, 35, 35, 21, 77, 514, 77, 21, 7, 749, 2611, 2611, 749, 7, 1, 972, 3937, 22440, 3937, 972, 1, 7, 127, 50334, 43308, 43308, 50334, 127, 7, 21, 3034, 4448, 1127514, 2250982, 1127514, 4448, 3034, 21, 35, 7161, 381982, 175865

Offset: 1

Author

R. H. Hardin Nov 26 2011

Keywords

• nonn
• tabl

Comments

Table starts

..7...21......35........35.........21.............7.............1

.21...70......35........77........749...........972...........127

.35...35.....514......2611.......3937.........50334..........4448

.35...77....2611.....22440......43308.......1127514........175865

.21..749....3937.....43308....2250982......11512566.......3558888

..7..972...50334...1127514...11512566......45244488......76714325

..1..127....4448....175865....3558888......76714325....1001060834

..7.3034..381982..20393189..473983329....4070916182...13053459189

.21.7161..206357..14766300.4102010820...93433967419..126679336122

.35.2170.1377351.158314010.3773723044.1001816580924.1146503112430

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

T(n,1) = binomial(7,n modulo 7). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).