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%I #23 Jul 02 2023 18:29:37
%S 1,1,1,3,3,5,9,9,15,27,27,45,81,81,135,243,243,405,729,729,1215,2187,
%T 2187,3645,6561,6561,10935,19683,19683,32805,59049,59049,98415,177147,
%U 177147,295245,531441,531441,885735,1594323,1594323,2657205,4782969,4782969
%N Maximum of odd products of partitions of n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 3).
%F For n>5, a(n+3) = 3a(n) (conjectured). - _Ralf Stephan_, Dec 02 2004
%F From _Ron Knott_, Mar 18 2020: (Start)
%F a(3*n) = 3^n; a(3*n+1) = a(3*n); a(3*n+2) = 5*3^(n-1) for n >= 1.
%F G.f.: -(2*x^5+x^2+x+1)/(3*x^3-1). (End)
%e 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.
%t 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 *)
%t Table[Max[(Times @@ #) & /@
%t IntegerPartitions[n, All, Range[1, n, 2]]], {n, 1, 43}]. (* _Ron Knott_, Mar 18 2020 *)
%Y Cf. A000792, A091915.
%K nonn
%O 0,4
%A _Jon Perry_, Feb 12 2004
%E More terms from _Robert G. Wilson v_, Feb 12 2004
%E a(0)=1 prepended by _Alois P. Heinz_, Mar 18 2020
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