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T(n,k)=Number of (n+1)X(k+1) 0..3 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i*x(i,j), i=1..n+1} nondecreasing
6

%I #4 Dec 02 2013 04:11:06

%S 83,527,578,2751,12920,3473,12556,235936,280325,18886,51716,3695555,

%T 18692802,5527323,95877,196332,51264185,1063222171,1359352910,

%U 100945688,462013,698368,644182816,53153482029,286526177537,91866009436,1735612787

%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i*x(i,j), i=1..n+1} nondecreasing

%C Table starts

%C ......83........527........2751........12556..........51716........196332

%C .....578......12920......235936......3695555.......51264185.....644182816

%C ....3473.....280325....18692802...1063222171....53153482029.2386893457725

%C ...18886....5527323..1359352910.286526177537.53047056275986

%C ...95877..100945688.91866009436

%C ..462013.1735612787

%C .2138895

%H R. H. Hardin, <a href="/A232886/b232886.txt">Table of n, a(n) for n = 1..32</a>

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 02 2013