A201142 T(n,k)=Number of nXk 0..5 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

6, 15, 15, 20, 30, 20, 15, 5, 5, 15, 6, 135, 402, 135, 6, 1, 282, 117, 117, 282, 1, 6, 51, 5252, 7642, 5252, 51, 6, 15, 848, 758, 38763, 38763, 758, 848, 15, 20, 1189, 35810, 13009, 129244, 13009, 35810, 1189, 20, 15, 120, 4788, 593543, 120096, 120096

Offset

1,1

Comments

Table starts

..6...15.....20.......15.........6..........1............6............15

.15...30......5......135.......282.........51..........848..........1189

.20....5....402......117......5252........758........35810..........4788

.15..135....117.....7642.....38763......13009.......593543.......2004404

..6..282...5252....38763....129244.....120096......4264060......46991775

..1...51....758....13009....120096....1268728......8360853......58395657

..6..848..35810...593543...4264060....8360853....543067656...11302225941

.15.1189...4788..2004404..46991775...58395657..11302225941..126701693572

.20..120.182640...480902.263910168..309819522.110916509158...83500574989

.15.2596..18486.17798640.769159517.1599103606.542120293937.9901442852486

Links

R. H. Hardin, Table of n, a(n) for n = 1..177

Formula

T(n,1) = binomial(6,n modulo 6). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

Example

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

Crossrefs

Sequence in context: A334352 A128512 A352098 * A200902 A205132 A199223

Adjacent sequences: A201139 A201140 A201141 * A201143 A201144 A201145

Keyword

nonn,tabl

Author

R. H. Hardin Nov 27 2011

Status

approved