A201503 - OEIS

%I #5 Mar 31 2012 12:36:44

%S 2,1,1,2,2,2,1,2,2,1,2,3,6,3,2,1,3,5,5,3,1,2,4,12,8,12,4,2,1,4,8,12,

%T 12,8,4,1,2,5,20,18,40,18,20,5,2,1,5,13,24,32,32,24,13,5,1,2,6,30,33,

%U 98,58,98,33,30,6,2,1,6,18,43,73,94,94,73,43,18,6,1,2,7,42,55,204,151,338,151,204

%N T(n,k)=Number of nXk 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

%C Table starts

%C .2.1..2..1...2...1...2....1....2....1....2.....1.....2.....1.....2......1

%C .1.2..2..3...3...4...4....5....5....6....6.....7.....7.....8.....8......9

%C .2.2..6..5..12...8..20...13...30...18...42....25....56....32....72.....41

%C .1.3..5..8..12..18..24...33...43...55...69....86...104...126...150....177

%C .2.3.12.12..40..32..98...73..204..141..380...252...650...414..1042....649

%C .1.4..8.18..32..58..94..151..227..338..480...676...920..1242..1636...2137

%C .2.4.20.24..98..94.338..289..936..734.2234..1656..4770..3370..9344...6375

%C .1.5.13.33..73.151.289..526..910.1514.2430..3788..5744..8512.12346..17575

%C .2.5.30.43.204.227.936..910.3334.2934.9936..8150.25908.20094.60882..45207

%C .1.6.18.55.141.338.734.1514.2934.5448.9686.16660.27718.44916.70922.109583

%H R. H. Hardin, <a href="/A201503/b201503.txt">Table of n, a(n) for n = 1..3037</a>

%e Some solutions for n=5 k=4

%e ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..0..0

%e ..0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..0....0..0..1..1

%e ..0..0..1..1....0..0..0..1....0..0..1..1....0..0..1..1....0..0..1..1

%e ..0..1..1..1....0..1..1..1....0..0..1..1....1..1..1..1....0..0..1..1

%e ..0..1..1..1....1..1..1..1....0..0..1..1....1..1..1..1....1..1..1..1

%Y Column 2 is A004526(n+2)

%Y Column 3 odd terms are A002378((n+1)/2)

%Y Column 3 even terms are A000982((n+2)/2)

%Y Column 4 is A001973

%Y Column 5 even terms are A188183((n-2)/2)

%Y Column 6 is A001977

%Y Column 7 even terms are A188185((n-4)/2)

%Y Column 8 is A001981

%Y Column 10 is A183913

%Y Column 12 is A183914

%Y Column 14 is A183915

%Y Column 16 is A183916

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Dec 02 2011