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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Michael Reid

Michael Reid's wiki page.

Michael Reid has authored 2 sequences.

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).

Original entry on oeis.org

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, 77373, 86759, 96972, 108063, 120080, 133067, 147082, 162174, 178395, 195806, 214461, 234421, 255739
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A000292 (for two permutations), A070736 (for four).
Cf. A072368 (three subsets of {1..3n})

Programs

  • Mathematica
    {1, 6}~Join~Table[Min[Map[Total,Map[#[[1]]*#[[2]]*#[[3]] &, Subsets[Permutations[Range[n]], {3}]]]] , {n, 3, 5}] (* Robert Price, Apr 08 2019 *)
(* OR, if allowed to replicate small permutations to account for n=1,2 *)
Table[ Min[Map[Total,Map[#[[1]]*#[[2]]*#[[3]] &,Subsets[If[n > 2, Permutations[Range[n]],Flatten[Table[Permutations[Range[n]], 3], 1]], {3}]]]] , {n, 1, 5}] (* Robert Price, Apr 09 2019 *)
  • PARI
    a(n) = {ret = 0; nb = n!; for (a=1, nb, pa = numtoperm(n, a); for (b=1, nb, pb = numtoperm(n, b); for (c=1, nb, pc = numtoperm(n, c); sp = sum(i=1, n, pa[i]*pb[i]*pc[i]); if (! ret, ret = sp, ret = min(ret, sp));););); return (ret);} \\ Michel Marcus, Jun 10 2013
  • Python
    # See Martin Fuller link, Aug 06 2023

Extensions

a(16)-a(19) from Hiroaki Yamanouchi, Aug 21 2015
a(20) onwards from Martin Fuller, Aug 06 2023

A070736 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).

Original entry on oeis.org

1, 8, 33, 96, 231, 484, 915, 1608, 2664, 4208, 6392, 9392, 13418, 18706, 25540, 34224, 45108, 58588, 75101, 95120, 119179, 147856, 181786, 221648, 268195, 322220, 384588, 456232, 538138, 631362, 737052, 856396, 990684, 1141254, 1309568, 1497104, 1705508, 1936416, 2191700, 2473248, 2783030
Offset: 1

Views

Author

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

Keywords

Examples

			Examples from _David A. Corneth_, Apr 09 2019:
a(1) = 1 via [1] [1] [1] [1];
a(2) = 8 via [1, 2] [1, 2] [2, 1] [2, 1];
a(3) = 33 via [1, 2, 3] [1, 3, 2] [3, 1, 2] [3, 2, 1];
a(4) = 96 via [1, 2, 3, 4] [2, 1, 4, 3] [3, 4, 1, 2] [4, 3, 2, 1];
a(5) = 231 via [1, 2, 3, 4, 5] [2, 3, 1, 4, 5] [4, 2, 5, 3, 1] [5, 4, 3, 1, 2];
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].

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • Python
    # See Martin Fuller link in A070735, Aug 06 2023

Extensions

a(11) onwards from Martin Fuller, Aug 06 2023

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