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%I #5 Mar 31 2012 12:36:58
%S 2278,12470,58048,230014,808455,2572189,7508980,20395251,51998196,
%T 125414516,287825519,631806642,1332124235,2708040628,5324902859,
%U 10157044643,18841255222,34065603378,60151407191,103913751089
%N Number of (n+1)X6 0..2 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 A203728
%H R. H. Hardin, <a href="/A203725/b203725.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) -21*a(n-2) +105*a(n-4) -168*a(n-5) -91*a(n-6) +512*a(n-7) -330*a(n-8) -560*a(n-9) +910*a(n-10) -910*a(n-12) +560*a(n-13) +330*a(n-14) -512*a(n-15) +91*a(n-16) +168*a(n-17) -105*a(n-18) +21*a(n-20) -8*a(n-21) +a(n-22) for n>30
%e Some solutions for n=4
%e ..1..2..1..1..1..1....0..0..0..2..2..2....2..2..2..2..2..2....1..1..2..1..1..2
%e ..2..1..2..2..2..2....0..1..2..2..2..2....2..2..2..2..2..2....0..2..1..2..2..2
%e ..1..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....1..1..2..2..2..2
%e ..1..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....0..2..2..2..2..2
%e ..2..2..2..2..2..2....2..2..2..2..2..2....2..2..2..2..2..2....0..2..2..2..2..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 05 2012