login
A371344
a(n)/144 is the minimum squared volume > 0 of a tetrahedron with integer edge lengths whose largest is n.
5
2, 11, 26, 47, 54, 107, 146, 191, 242, 299, 191, 134, 146, 146, 151, 767, 423, 151, 854, 558, 764, 491, 503, 464, 146, 146, 431, 944, 666, 146, 146, 350, 146, 311, 599, 511, 1559, 599, 944, 1871, 1679, 990, 1375, 1907, 990, 551, 959, 1199, 1244, 990, 1206, 854, 764
OFFSET
1,1
LINKS
Sascha Kurz, Enumeration of integral tetrahedra, arXiv:0804.1310 [math.CO], 2008.
Hugo Pfoertner, Plot of log_10(n) vs n, using Plot 2.
EXAMPLE
a(1) = 2 corresponds to the regular tetrahedron with all edges equal to 1. Its volume is sqrt(2/144) = 0.11785113...
PROG
(PARI) \\ See A371345. Replace final #Set(Vec(L)) by vecmin(Vec(L))/2
\\ Second version using simple minded loops and triangle inequalities
\\ Not suitable for larger n
a371344(n) = {my (Vmin=oo, w=vector(6)); w[1]=n; for(w2=1, n, w[2]=w2; for(w3=1, n, w[3]=w3; for(w4=1, n, w[4]=w4; for(w5=1, n, w[5]=w5; for(w6=1, n, w[6]=w6;
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)))))))); Vmin};
CROSSREFS
Subset of A371071.
A001014(n)/72 are the corresponding maximum squared volumes.
Sequence in context: A296285 A077482 A141428 * A104085 A080663 A248118
KEYWORD
nonn,look
AUTHOR
Hugo Pfoertner, Mar 19 2024
STATUS
approved