三元组和的最小值

王守恩

a(1)=1,  1×1×1=1,
1,
1,
1,

a(2)=6,  1×2×2+2×1×1=6,
1,2,
2,1,
2,1,

a(3)=18,  1×3×2+2×1×3+3×2×1=18,
1,2,3,
3,1,2,
2,3,1,

a(4)=44,  1×4×3+2×2×2+3×1×4+4×3×1=44,
1,2,3,4,
4,2,1,3,
3,2,4,1,

a(5)=89,  1×5×3+2×2×4+3×3×2+4×1×5+5×4×1=89,
1,2,3,4,5,
5,2,3,1,4,
3,4,2,5,1,

a(6)=162,  1×6×5+2×4×3+3×2×4+4×3×2+5×1×6+6×5×1=162,
1,2,3,4,5,6,
6,4,2,3,1,5,
5,3,4,2,6,1,

a(7)=271,  1×7×5+2×5×4+3×2×6+4×3×3+5×4×2+6×1×7+7×6×1=271,
1,2,3,4,5,6,7,
7,5,2,3,4,1,6,
5,4,6,3,2,7,1,

a(8)=428,  1×8×7+2×5×5+3×3×6+4×4×3+5×6×2+6×2×4+7×1×8+8×7×1=428,
1,2,3,4,5,6,7,8,
8,5,3,4,6,2,1,7,
7,5,6,3,2,4,8,1,

a(9)=642,  ——OEIS没有这些详细资料。
......

1, 6, 18, 44, 89, 162, 271, 428, 642, 930, 1304, 1781, 2377, 3111, 4002, 5073, 6344, 7842, 9587, 11610, 13933, 16591, 19612, 23028, 26871, 31177, 35976, 41314, 47221, 53736, 60907, 68773, ——a(204)。

A070735——Let r, s, t be three permutations of the set { 1, 2, 3, ..., n }; a(n) = minimal value of Sum_{i=1..n} r(i)*s(i)*t(i).

a(16)-a(19) from Hiroaki Yamanouchi, Aug 21 2015

a(20) onwards from Martin Fuller, Aug 06 2023

Martin Fuller, Table of n, a(n) for n = 1..204——记住: "Martin Fuller"——这是个"狠角色"—— 一下子冲到a(204)。