OFFSET
0,4
COMMENTS
a(n) is the greatest number in row n of A048996 and in row n of A072811. Thus a(n) is the greatest number of compositions (permutations) obtainable from some partition of n. Example: a(7)=12 is the greatest number of compositions from some partition of 7, specifically, the partition {3,2,1,1}. - Clark Kimberling, Dec 24 2006
The partition(s) giving this optimum is always one where #{parts equal to i} >= #{parts equal to j} if i <= j. These partitions are counted in A007294. - Franklin T. Adams-Watters, Apr 08 2008
The number of partition(s) giving this optimum is given by A198254. - Olivier Gérard, Nov 17 2011
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0 or i=1, (p+n)!/n!,
max(seq(b(n-i*j, i-1, p+j)/j!, j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50); # Alois P. Heinz, Apr 15 2015
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[n == 0 || i == 1, (p + n)!/n!, Max[Table[ b[n-i*j, i-1, p+j]/j!, {j, 0, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 19 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 23 2005
STATUS
approved