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A371072
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a(n)/144 is the minimum squared volume > 0 of a tetrahedron with the sum of its integer edge lengths equal to n.
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4
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11, 14, 44, 26, 59, 34, 47, 126, 119, 62, 215, 54, 107, 98, 243, 146, 335, 142, 191, 614, 479, 194, 764, 423, 299, 254, 1004, 239, 851, 322, 304, 783, 887, 134, 479, 1719, 315, 234, 1196, 191, 896, 574, 767, 1127, 151, 674, 956, 956, 671, 146, 1391, 1082, 791, 898, 263, 1184, 151
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OFFSET
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9,1
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COMMENTS
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a(6) = 2, but since there are no tetrahedra with volume > 0 for n=7 and n=8, the offset 9 is chosen.
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LINKS
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PROG
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(PARI) a371072(n) = {my (Vmin=oo); forpart (w=n, forperm (w, v, if(v[4]+v[5]<v[6], next); if(v[4]+v[6]<v[5], next); if(v[5]+v[6]<v[4], next); if(v[1]+v[2]<v[4], next); if(v[1]+v[4]<v[2], next); if(v[2]+v[4]<v[1], next); if(v[1]+v[3]<v[5], next); if(v[1]+v[5]<v[3], next); if(v[3]+v[5]<v[1], next); if(v[2]+v[3]<v[6], next); if(v[2]+v[6]<v[3], next); if(v[3]+v[6]<v[2], next); my(CM=matdet ([0, 1, 1, 1, 1; 1, 0, v[1]^2, v[2]^2, v[3]^2; 1, v[1]^2, 0, v[4]^2, v[5]^2; 1, v[2]^2, v[4]^2, 0, v[6]^2; 1, v[3]^2, v[5]^2, v[6]^2, 0])); if (CM>0, Vmin=min(Vmin, CM))), [1, n], [6, 6]); Vmin/2};
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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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