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%I #5 May 17 2021 15:12:06
%S 3362,256099,15632055,792134993,34363298528,1305785141000,
%T 44235742136926,1354583560472552,37913976382125298
%N Number of (3+1) X (n+1) 0..3 arrays x(i,j) with row sums Sum_{j=1..n+1} x(i,j) nondecreasing, and column sums Sum_{i=1..3+1} i^2*x(i,j) nondecreasing.
%C Row 3 of A233353.
%e Some solutions for n=2
%e ..0..0..2....0..0..0....0..1..0....0..0..2....0..0..1....2..0..2....2..0..0
%e ..0..1..2....1..2..1....0..1..0....1..0..2....2..2..0....1..3..3....3..0..0
%e ..1..2..0....0..2..2....0..0..3....0..2..2....1..1..3....1..3..3....0..1..3
%e ..1..1..2....1..1..3....2..3..2....3..3..3....1..2..3....3..3..3....1..2..1
%Y Cf. A233353.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 07 2013