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%I #5 Mar 31 2012 12:36:58
%S 565,10109,187118,2903185,38244007,439011778,4495376717,41798687510,
%T 357812176251,2850828614967,21326952334327,150893156035616,
%U 1015825365550770,6540355133421706,40450295862176890,241228558744536682
%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) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing
%C Column 2 of A203787
%H R. H. Hardin, <a href="/A203781/b203781.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 55*a(n-1) -1440*a(n-2) +23852*a(n-3) -280076*a(n-4) +2474460*a(n-5) -17024052*a(n-6) +92995860*a(n-7) -406626336*a(n-8) +1417827048*a(n-9) -3856529652*a(n-10) +7670112516*a(n-11) -8738530620*a(n-12) -5208244788*a(n-13) +50153902524*a(n-14) -118298746716*a(n-15) +134937662118*a(n-16) +33490877310*a(n-17) -429636601924*a(n-18) +772811055052*a(n-19) -484068870036*a(n-20) -717113206876*a(n-21) +2049391909540*a(n-22) -1905937835076*a(n-23) -429232892712*a(n-24) +3256097340336*a(n-25) -3579343666524*a(n-26) +467095009260*a(n-27) +3310697961996*a(n-28) -4022945360028*a(n-29) +1162694578452*a(n-30) +2130146612364*a(n-31) -2827734318045*a(n-32) +1080655080243*a(n-33) +783566461236*a(n-34) -1212250161384*a(n-35) +557760264272*a(n-36) +105098522320*a(n-37) -283726633536*a(n-38) +158118019328*a(n-39) -22871890688*a(n-40) -23641277184*a(n-41) +18825661440*a(n-42) -7095085056*a(n-43) +1593520128*a(n-44) -206032896*a(n-45) +11943936*a(n-46) for n>51
%e Some solutions for n=4
%e ..1..1..2....2..1..1....3..0..1....0..1..0....3..0..1....3..1..1....0..3..3
%e ..1..1..2....0..3..3....0..3..2....0..1..3....0..3..2....1..3..3....1..3..3
%e ..1..3..2....2..2..2....3..1..2....1..1..2....1..2..3....1..3..3....2..3..3
%e ..3..2..0....1..3..3....1..3..3....0..2..1....2..3..3....3..2..2....2..3..3
%e ..2..3..1....1..3..3....1..3..3....0..2..1....2..3..3....2..3..3....3..3..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 05 2012
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