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%I #5 Mar 31 2012 12:36:58
%S 31942,488745,5538127,47229554,325435792,1908258519,9804436984,
%T 45182796559,189566445222,733391349143,2640507039363,8918429929980,
%U 28437223041567,86078536752689,248504972893078,687066519837963
%N Number of (n+1)X6 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 5 of A203741
%H R. H. Hardin, <a href="/A203738/b203738.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 15*a(n-1) -89*a(n-2) +216*a(n-3) +181*a(n-4) -2401*a(n-5) +4641*a(n-6) +4328*a(n-7) -31187*a(n-8) +31993*a(n-9) +71773*a(n-10) -202592*a(n-11) +30303*a(n-12) +510433*a(n-13) -600277*a(n-14) -541920*a(n-15) +1681958*a(n-16) -435434*a(n-17) -2440234*a(n-18) +2491216*a(n-19) +1618722*a(n-20) -4268394*a(n-21) +848250*a(n-22) +4071600*a(n-23) -3223350*a(n-24) -1893294*a(n-25) +3708810*a(n-26) -461216*a(n-27) -2380146*a(n-28) +1432514*a(n-29) +744966*a(n-30) -1100896*a(n-31) +105547*a(n-32) +446187*a(n-33) -220493*a(n-34) -76648*a(n-35) +100217*a(n-36) -14053*a(n-37) -20683*a(n-38) +10152*a(n-39) +665*a(n-40) -1883*a(n-41) +489*a(n-42) +64*a(n-43) -61*a(n-44) +13*a(n-45) -a(n-46) for n>60
%e Some solutions for n=4
%e ..1..1..3..2..2..2....3..3..3..3..3..3....1..0..0..3..1..2....1..0..3..1..1..3
%e ..0..2..2..3..3..3....3..3..3..3..3..3....0..1..2..1..3..2....0..3..1..3..3..3
%e ..3..1..3..3..3..3....3..3..3..3..3..3....0..2..1..3..2..3....2..1..3..3..3..3
%e ..1..3..3..3..3..3....3..3..3..3..3..3....2..0..3..2..3..2....0..3..3..3..3..3
%e ..1..3..3..3..3..3....3..3..3..3..3..3....0..2..2..3..2..3....0..3..3..3..3..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 05 2012
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