A201142 - OEIS

%I #5 Mar 31 2012 12:36:43

%S 6,15,15,20,30,20,15,5,5,15,6,135,402,135,6,1,282,117,117,282,1,6,51,

%T 5252,7642,5252,51,6,15,848,758,38763,38763,758,848,15,20,1189,35810,

%U 13009,129244,13009,35810,1189,20,15,120,4788,593543,120096,120096

%N 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

%C Table starts

%C ..6...15.....20.......15.........6..........1............6............15

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

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

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

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

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

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

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

%C .20..120.182640...480902.263910168..309819522.110916509158...83500574989

%C .15.2596..18486.17798640.769159517.1599103606.542120293937.9901442852486

%H R. H. Hardin, <a href="/A201142/b201142.txt">Table of n, a(n) for n = 1..177</a>

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

%e Some solutions for n=3 k=7

%e ..0..0..0..1..1..4..4....0..0..0..0..1..1..3....0..0..1..2..3..3..4

%e ..0..2..2..3..3..4..5....1..2..2..2..3..3..5....0..1..2..3..4..4..4

%e ..1..2..2..3..5..5..5....3..4..4..4..5..5..5....0..1..2..3..5..5..5

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 27 2011