

A091916


Maximum of odd products of partitions of n.


1



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
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OFFSET

0,4


LINKS

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


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^(n1) for n >= 1.
G.f.: (2*x^5+x^2+x+1)/(3*x^31). (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



