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%I #6 Mar 31 2012 12:36:57
%S 1212,27966,557544,9592248,146861704,2050339423,26569429480,
%T 323824032048,3749613354500,41576091707436,444241382108136,
%U 4597646074173360,46283153123300304,454783873288441005,4374858039450660168
%N Number of (n+1)X2 0..7 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 A203661
%H R. H. Hardin, <a href="/A203657/b203657.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 70*a(n-1) -2275*a(n-2) +45612*a(n-3) -632289*a(n-4) +6438138*a(n-5) -49938467*a(n-6) +302065016*a(n-7) -1446908771*a(n-8) +5543625850*a(n-9) -17090839633*a(n-10) +42516502924*a(n-11) -85337511267*a(n-12) +137796276966*a(n-13) -177910179993*a(n-14) +181835622416*a(n-15) -144879499352*a(n-16) +87918207776*a(n-17) -39188297232*a(n-18) +12080293632*a(n-19) -2298481920*a(n-20) +203212800*a(n-21)
%e Some solutions for n=5
%e ..6..1....1..1....7..2....0..5....0..2....5..2....2..3....7..7....6..6....0..3
%e ..1..6....3..3....2..7....2..3....5..3....1..6....2..7....7..7....5..7....3..4
%e ..2..5....4..4....2..7....7..0....5..7....7..2....5..4....7..7....5..7....5..2
%e ..3..4....5..5....2..7....0..7....5..7....2..7....2..7....7..7....5..7....5..2
%e ..0..7....6..7....3..6....3..4....5..7....2..7....7..2....7..7....7..5....1..6
%e ..1..6....6..7....4..5....2..5....5..7....5..4....7..5....7..7....5..7....0..7
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 04 2012
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