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%I #5 Mar 31 2012 12:36:58
%S 499,3912,23442,114276,488745,1868452,6571172,21530128,66630375,
%T 196405354,555736019,1517903362,4021656843,10375637542,26152033020,
%U 64573262520,156555567431,373428801166,877831497249,2036649664260
%N Number of (n+1)X3 0..3 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively
%C Column 2 of A203741
%H R. H. Hardin, <a href="/A203735/b203735.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -64*a(n-2) +112*a(n-3) +193*a(n-4) -1145*a(n-5) +1171*a(n-6) +2815*a(n-7) -7600*a(n-8) +620*a(n-9) +17570*a(n-10) -16376*a(n-11) -18514*a(n-12) +37522*a(n-13) +1693*a(n-14) -44011*a(n-15) +19988*a(n-16) +29252*a(n-17) -26851*a(n-18) -9189*a(n-19) +18134*a(n-20) -1082*a(n-21) -7142*a(n-22) +2176*a(n-23) +1569*a(n-24) -849*a(n-25) -139*a(n-26) +153*a(n-27) -9*a(n-28) -11*a(n-29) +2*a(n-30) for n>32
%e Some solutions for n=4
%e ..3..1..1....3..2..2....3..2..3....0..3..3....3..3..3....2..2..2....0..0..1
%e ..1..3..3....2..3..3....2..3..2....0..3..3....3..3..3....3..3..3....0..3..2
%e ..1..3..3....2..3..3....3..2..3....2..3..3....3..3..3....3..3..3....1..2..3
%e ..1..3..3....3..3..3....2..3..3....2..3..3....3..3..3....3..3..3....0..3..2
%e ..2..3..3....3..3..3....2..3..3....3..3..3....3..3..3....3..3..3....3..2..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 05 2012
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