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%I #5 Mar 31 2012 12:37:01
%S 1212,22294,296860,3478214,35861109,338578395,2968107693,24512819961,
%T 192534548713,1449555741972,10524783969235,74063987250838,
%U 507210250807025,3391824829301973,22211886605224671,142790417728047259
%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) nondecreasing in column and row directions, respectively
%C Column 1 of A204339
%H R. H. Hardin, <a href="/A204332/b204332.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 36*a(n-1) -546*a(n-2) +4326*a(n-3) -16317*a(n-4) -5586*a(n-5) +315247*a(n-6) -1018269*a(n-7) -939676*a(n-8) +12704572*a(n-9) -16661906*a(n-10) -69575080*a(n-11) +209055413*a(n-12) +156695364*a(n-13) -1243866973*a(n-14) +385394353*a(n-15) +4799309697*a(n-16) -4619572562*a(n-17) -13110243036*a(n-18) +20376494246*a(n-19) +26024019591*a(n-20) -59676249008*a(n-21) -36648445840*a(n-22) +130898297148*a(n-23) +31360713560*a(n-24) -226218692054*a(n-25) +960555918*a(n-26) +316702368069*a(n-27) -56116682690*a(n-28) -365472332020*a(n-29) +112266366855*a(n-30) +351712476801*a(n-31) -143886946102*a(n-32) -284512647569*a(n-33) +139881792382*a(n-34) +194491688712*a(n-35) -108967065914*a(n-36) -112716095553*a(n-37) +69716304614*a(n-38) +55459081302*a(n-39) -37093140255*a(n-40) -23160095462*a(n-41) +16512431452*a(n-42) +8192514257*a(n-43) -6162056301*a(n-44) -2445170981*a(n-45) +1925152191*a(n-46) +612011574*a(n-47) -501348866*a(n-48) -127324434*a(n-49) +108003437*a(n-50) +21743039*a(n-51) -19024290*a(n-52) -2994334*a(n-53) +2693788*a(n-54) +324175*a(n-55) -299058*a(n-56) -26552*a(n-57) +25061*a(n-58) +1546*a(n-59) -1490*a(n-60) -57*a(n-61) +56*a(n-62) +a(n-63) -a(n-64)
%e Some solutions for n=4
%e ..5..4....4..1....1..5....5..3....5..0....0..3....2..5....0..7....0..0....3..7
%e ..4..5....1..7....7..3....1..7....2..7....1..2....0..7....0..7....5..5....4..6
%e ..2..7....7..1....3..7....4..5....5..4....2..1....7..0....1..6....3..7....6..4
%e ..5..4....1..7....7..3....4..5....3..6....6..7....0..7....4..3....6..6....3..7
%e ..5..6....1..7....3..7....5..4....4..5....6..7....7..2....6..7....5..7....3..7
%K nonn
%O 1,1
%A _R. H. Hardin_ Jan 14 2012
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