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A072368
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Minimal total volume of n bricks with integer sides, all sides being different. Lowest value of sum of products of triples p*q*r chosen from [1,3n].
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3
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6, 54, 214, 594, 1334, 2614, 4645, 7676, 11992, 17912, 25791, 36021, 49028, 65269, 85247, 109493, 138575, 173094, 213694, 261048, 315863, 378888, 450907, 532730, 625213, 729244, 845748, 975679, 1120035, 1279848, 1456176, 1650123, 1862831, 2095469, 2349237
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OFFSET
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1,1
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COMMENTS
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For n=19, the smallest integer from each triple does not belong to range [1,19]. Triplicating the sets of triples, shifting each triple to the left, generates permutations as in A070735, but not provably minimal ones.
a(n) >= ceiling(n*(3n!)^(1/n)) with the inequality tight for 1 <= n <= 3. - Chai Wah Wu, Mar 05 2020
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LINKS
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EXAMPLE
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a(7)=4645 because (1*20*21)+(2*18*19)+(3*15*16)+(4*13*14)+(5*8*17)+(6*10*12)+(7*9*11)=4645 is the smallest value attainable.
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PROG
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(Python) See Martin Fuller link
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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Corrected and extended via integer linear programming by Rob Pratt, Jul 28 2023
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STATUS
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approved
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