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A202028
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Number of nX3 zero-sum -1..1 arrays with rows and columns lexicographically nondecreasing
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1
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2, 21, 181, 1341, 8312, 44300, 207562, 872998, 3348194, 11857834, 39165935, 121628739, 357500769, 1000121700, 2675524936, 6872220036, 17006979680, 40673780258, 94256429647, 212145160692, 464710684230, 992576762139
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) +6*a(n-2) -6*a(n-3) -24*a(n-4) -15*a(n-5) +56*a(n-6) +116*a(n-7) +15*a(n-8) -240*a(n-9) -405*a(n-10) -60*a(n-11) +754*a(n-12) +1219*a(n-13) +360*a(n-14) -1745*a(n-15) -3146*a(n-16) -1602*a(n-17) +2909*a(n-18) +6800*a(n-19) +5196*a(n-20) -2948*a(n-21) -11972*a(n-22) -12609*a(n-23) -791*a(n-24) +16396*a(n-25) +23832*a(n-26) +11124*a(n-27) -15648*a(n-28) -35421*a(n-29) -28174*a(n-30) +5318*a(n-31) +40566*a(n-32) +47078*a(n-33) +14999*a(n-34) -33180*a(n-35) -58924*a(n-36) -38992*a(n-37) +12912*a(n-38) +56245*a(n-39) +56245*a(n-40) +12912*a(n-41) -38992*a(n-42) -58924*a(n-43) -33180*a(n-44) +14999*a(n-45) +47078*a(n-46) +40566*a(n-47) +5318*a(n-48) -28174*a(n-49) -35421*a(n-50) -15648*a(n-51) +11124*a(n-52) +23832*a(n-53) +16396*a(n-54) -791*a(n-55) -12609*a(n-56) -11972*a(n-57) -2948*a(n-58) +5196*a(n-59) +6800*a(n-60) +2909*a(n-61) -1602*a(n-62) -3146*a(n-63) -1745*a(n-64) +360*a(n-65) +1219*a(n-66) +754*a(n-67) -60*a(n-68) -405*a(n-69) -240*a(n-70) +15*a(n-71) +116*a(n-72) +56*a(n-73) -15*a(n-74) -24*a(n-75) -6*a(n-76) +6*a(n-77) +2*a(n-78) -a(n-79)
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EXAMPLE
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Some solutions for n=6
.-1.-1..1...-1.-1..0...-1.-1.-1...-1..0..0...-1.-1..0...-1.-1..0...-1.-1.-1
.-1..1..1...-1..1..0...-1..0..1....0.-1.-1...-1..1..1...-1..1..0...-1..1..1
.-1..1..1...-1..1..0....0..1.-1....0.-1..1....0.-1.-1....0..0..1....0.-1..1
..0.-1..1...-1..1..1....0..1..0....0..1..1....1..0..0....1.-1..0....0..0..0
..0..0.-1....1.-1.-1....1.-1..1....1.-1.-1....1..0..0....1.-1..1....0..1..0
..0..0..0....1..1..0....1.-1..1....1..0..1....1..0..0....1..0.-1....1..1.-1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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