A091916 Maximum of odd products of partitions of n.

1, 1, 1, 3, 3, 5, 9, 9, 15, 27, 27, 45, 81, 81, 135, 243, 243, 405, 729, 729, 1215, 2187, 2187, 3645, 6561, 6561, 10935, 19683, 19683, 32805, 59049, 59049, 98415, 177147, 177147, 295245, 531441, 531441, 885735, 1594323, 1594323, 2657205, 4782969, 4782969

Offset

0,4

Links

Table of n, a(n) for n=0..43.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 3).

Formula

For n>5, a(n+3) = 3a(n) (conjectured). - Ralf Stephan, Dec 02 2004

From Ron Knott, Mar 18 2020: (Start)

a(3*n) = 3^n; a(3*n+1) = a(3*n); a(3*n+2) = 5*3^(n-1) for n >= 1.

G.f.: -(2*x^5+x^2+x+1)/(3*x^3-1). (End)

Example

The partitions of 5 are 5, 41, 32, 311, 221, 2111, 11111, with products 5, 4, 6, 3, 4, 2, 1 and the maximal odd product is 5.

Mathematica

first Needs["DiscreteMath`Combinatorica`"], then f[n_] := Max[ Select[ Apply[ Times, Partitions[n], 2], OddQ[ # ] &]]; Table[ f[n], {n, 1, 43}] (* Robert G. Wilson v, Feb 12 2004 *)
Table[Max[(Times @@ #) & /@
IntegerPartitions[n, All, Range[1, n, 2]]], {n, 1, 43}]. (* Ron Knott, Mar 18 2020 *)

Crossrefs

Cf. A000792, A091915.

Sequence in context: A179437 A136791 A213933 * A102437 A319794 A072706

Adjacent sequences: A091913 A091914 A091915 * A091917 A091918 A091919

Keyword

nonn

Author

Jon Perry, Feb 12 2004

Extensions

More terms from Robert G. Wilson v, Feb 12 2004

a(0)=1 prepended by Alois P. Heinz, Mar 18 2020

Status

approved