A088881 If A056239(m) = n, then a(n) is the maximum value of A000005(m).

1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 24, 30, 36, 42, 48, 60, 72, 84, 96, 112, 128, 144, 168, 192, 224, 256, 288, 336, 384, 432, 480, 540, 600, 672, 768, 864, 960, 1080, 1200, 1320, 1440, 1620, 1800, 1980, 2160, 2400, 2640, 2880, 3240, 3600, 3960, 4320, 4800, 5280

Offset

0,2

Comments

Maximum number of submultisets among all integer partitions of n. - Gus Wiseman, Jun 30 2019

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

The partition (3,2,1,1,1) has 16 submultisets, which is more than for any other partition of 8, so a(8) = 16. - Gus Wiseman, Jun 30 2019

Maple

b:= proc(n, i) option remember; `if`(n=0 or i<2, n+1,
       max(seq((j+1)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> b(n, n):
seq (a(n), n=0..100);  # Alois P. Heinz, Aug 09 2012

Mathematica

$RecursionLimit = 1000; b[n_, i_] :=  b[n, i] = If[n == 0 || i<2, n+1, Max[Table[ (j+1)*b[n-i*j, i-1], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table [a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 15 2015, after Alois P. Heinz *)
Table[Max@@(Times@@(1+Length/@Split[#])&)/@IntegerPartitions[n], {n, 0, 30}] (* Gus Wiseman, Jun 30 2019 *)

Crossrefs

Cf. A088880, A307699, A325694, A325798, A325828, A325830, A325831, A325832, A325833, A325834.

Sequence in context: A191283 A341016 A200678 * A020697 A175381 A369519

Adjacent sequences: A088878 A088879 A088880 * A088882 A088883 A088884

Keyword

easy,nonn

Author

Naohiro Nomoto, Nov 28 2003

Status

approved