[seqfan] Re: next partition into distinct parts

[wouter meeussen]

It is slightly surprising that the odd and strict partitions occur at near
regular positions in the reverse lexicographic ordering.
Moreover, they generate sequences that are either "thin" (no GF, no
references) or absent in OEIS:

Positions of the odd partitions (seem to) converge to A035399 (Olivier
Gerard)
"Related to partitions without repetitions",

Positions of the even partitions of odd n (seem to) converge to
{1, 4, 9, 12, 21, 24, 26, 30, 47, 50, 52, 59, 62, 67, 99, 102, 104, 110,
 113, 116, 126, 129, 133, 139, 197, 200, 202, 208, 211, 214, 227, 231,
 234, 238, 254, 256, 260, 265, 272, ...

Positions of the even partitions of even n (seem to) converge to
{2, 5, 7, 13, 16, 19, 31, 34, 38, 41, 45, 68, 71, 76, 79, 86, 88, 92, 97,
 140, 143, 148, 151, 159, 162, 164, 168, 181, 184, 189, 195, 273, 276,
 281, 284, 293, 296, 298, 302, 317, 319, 326, 329, 334, 353, 356, 360, 366,
373, ...

Wouter.

>
> Does anyone out there have a Mathematica program which will give the
> next partition into distinct parts?
>