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%I #6 Mar 31 2012 12:36:57
%S 406,5411,64568,680400,6489940,57269565,475164554,3751457500,
%T 28439396482,208468893647,1485783530684,10341422407224,70546056791520,
%U 473056332125577,3125814445750542,20394520446794452,131617722687439662
%N Number of (n+1)X2 0..5 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 1 of A203714
%H R. H. Hardin, <a href="/A203710/b203710.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 40*a(n-1) -725*a(n-2) +7890*a(n-3) -57598*a(n-4) +298496*a(n-5) -1133650*a(n-6) +3211340*a(n-7) -6839701*a(n-8) +10954608*a(n-9) -13092665*a(n-10) +11477170*a(n-11) -7151500*a(n-12) +2994456*a(n-13) -754560*a(n-14) +86400*a(n-15)
%e Some solutions for n=4
%e ..2..1....1..2....4..3....2..0....5..4....0..5....2..4....5..3....5..1....5..3
%e ..4..5....1..5....2..5....3..5....4..5....0..5....2..4....3..5....1..5....3..5
%e ..4..5....1..5....4..3....3..5....4..5....3..3....5..5....4..4....1..5....3..5
%e ..4..5....4..2....2..5....3..5....4..5....1..5....5..5....3..5....1..5....3..5
%e ..4..5....3..3....5..3....3..5....4..5....3..3....5..5....5..3....4..2....3..5
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 04 2012
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