OFFSET
9,1
COMMENTS
a(6) = 2, but since there are no tetrahedra with volume > 0 for n=7 and n=8, the offset 9 is chosen.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 9..150
PROG
(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};
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Mar 19 2024
STATUS
approved