A070736 - OEIS

%I #25 Aug 08 2023 10:06:04

%S 1,8,33,96,231,484,915,1608,2664,4208,6392,9392,13418,18706,25540,

%T 34224,45108,58588,75101,95120,119179,147856,181786,221648,268195,

%U 322220,384588,456232,538138,631362,737052,856396,990684,1141254,1309568,1497104,1705508,1936416,2191700,2473248,2783030

%N Let r, s, t, u be four permutations of the set { 1, 2, 3, ..., n }; a(n) = minimal value of Sum_{i=1..n} r(i)*s(i)*t(i)*u(i).

%H Martin Fuller, <a href="/A070736/b070736.txt">Table of n, a(n) for n = 1..100</a>

%e Examples from _David A. Corneth_, Apr 09 2019:

%e a(1) = 1 via [1] [1] [1] [1];

%e a(2) = 8 via [1, 2] [1, 2] [2, 1] [2, 1];

%e a(3) = 33 via [1, 2, 3] [1, 3, 2] [3, 1, 2] [3, 2, 1];

%e a(4) = 96 via [1, 2, 3, 4] [2, 1, 4, 3] [3, 4, 1, 2] [4, 3, 2, 1];

%e a(5) = 231 via [1, 2, 3, 4, 5] [2, 3, 1, 4, 5] [4, 2, 5, 3, 1] [5, 4, 3, 1, 2];

%e a(6) = 484 via [1, 2, 3, 4, 5, 6] [2, 3, 5, 1, 4, 6] [6, 3, 2, 5, 4, 1] [6, 5, 3, 4, 1, 2].

%t Table[Min[Map[Total,Map[#[[1]]*#[[2]]*#[[3]]*#[[4]] &,Subsets[If[n > 3, Permutations[Range[n]],Flatten[Table[Permutations[Range[n]], 4], 1]], {4}]]]] , {n, 1, 5}] (* _Robert Price_, Apr 09 2019 *)

%o (Python) # See Martin Fuller link in A070735, Aug 06 2023

%Y Cf. A000292 (for two permutations), A070735 (for three).

%K nice,nonn,hard

%O 1,2

%A Michael Reid (mreid(AT)math.umass.edu), May 15 2002

%E a(11) onwards from _Martin Fuller_, Aug 06 2023