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%I #5 Mar 31 2012 12:36:57
%S 128,376,4200,46853,554620,5972476,58336803,513856445,4101307146,
%T 29848597757,199510291989,1233383781223,7098573840897,38262130398415,
%U 194182080859393,932300124491835,4252520574236931,18497724390086100
%N Number of (n+1)X6 0..1 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) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
%C Column 5 of A203452
%H R. H. Hardin, <a href="/A203449/b203449.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 55*a(n-1) -1483*a(n-2) +26127*a(n-3) -338193*a(n-4) +3429153*a(n-5) -28357173*a(n-6) +196602705*a(n-7) -1165912020*a(n-8) +6004200930*a(n-9) -27167717850*a(n-10) +109017693330*a(n-11) -390868315110*a(n-12) +1259737285590*a(n-13) -3667535195310*a(n-14) +9683348321430*a(n-15) -23258505573135*a(n-16) +50939627117085*a(n-17) -101889860027865*a(n-18) +186269554665285*a(n-19) -311184592804995*a(n-20) +474428969358435*a(n-21) -658078892981055*a(n-22) +825759258027795*a(n-23) -927565193949030*a(n-24) +913991069159532*a(n-25) -755278225466940*a(n-26) +457962352584716*a(n-27) -69533550916004*a(n-28) -333281502666364*a(n-29) +668960713985004*a(n-30) -877793403054204*a(n-31) +938876964606945*a(n-32) -871006340659455*a(n-33) +719295534188595*a(n-34) -535645610565975*a(n-35) +362198460477945*a(n-36) -223220139898665*a(n-37) +125604414729885*a(n-38) -64557466221465*a(n-39) +30290146792920*a(n-40) -12955106337390*a(n-41) +5039562750390*a(n-42) -1777622462910*a(n-43) +566360211690*a(n-44) -162197055930*a(n-45) +41503024290*a(n-46) -9418306170*a(n-47) +1878003855*a(n-48) -325211445*a(n-49) +48175569*a(n-50) -5983965*a(n-51) +606267*a(n-52) -48123*a(n-53) +2807*a(n-54) -107*a(n-55) +2*a(n-56) for n>79
%e Some solutions for n=4
%e ..0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..1..0
%e ..0..0..0..1..1..1....0..0..0..0..0..1....0..0..0..0..0..1....0..0..1..1..0..1
%e ..0..0..1..0..0..1....0..0..0..0..0..1....0..0..0..1..1..1....0..1..0..0..1..1
%e ..1..1..0..0..1..0....0..0..1..1..1..0....0..0..1..1..1..1....1..0..1..1..1..1
%e ..1..1..1..0..0..0....0..0..1..1..1..1....1..1..0..0..0..1....0..1..1..1..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 02 2012
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