A179817 Maximally refined partitions into distinct parts (of any natural number) with n parts.

1, 2, 4, 8, 14, 27, 48, 86, 151, 269, 460, 808, 1386, 2372, 4048, 6890, 11661, 19719, 33167, 55705, 93288, 155954, 260040, 432895, 719252, 1192989, 1975724, 3267513, 5396171, 8900534, 14663096

Offset

0,2

Comments

For the definition, see sequence A179009. This sequence counts the same objects using a different statistic, the number of parts rather than their sum.

Links

Table of n, a(n) for n=0..30.

Example

For n=2, the partitions being counted are:
  2+1, 3+1, 4+1, 3+2.
For n=3, the partitions are:
  3+2+1, 4+2+1, 5+2+1, 6+2+1,
  4+3+1, 5+3+1, 6+4+1, 4+3+2.

Prog

(PARI)
ok(k, b)={for(i=1, (k-1)\2, if(bittest(b, i) && bittest(b, k-i), return(0))); 1}
a(n)={((k, w, b)->if(w==n, 1, if(k<=2*w+1, self()(k+1, w, bitor(b, 1<<k))) + if(ok(k, b), self()(k+1, w+1, b))))(1, 0, 0)} \\ Andrew Howroyd, Apr 14 2021

Crossrefs

Cf. A179009, A179822.

Sequence in context: A068011 A048238 A048140 * A214255 A065616 A164147

Adjacent sequences: A179814 A179815 A179816 * A179818 A179819 A179820

Keyword

nonn,more

Author

Moshe Shmuel Newman, Jan 10 2011

Extensions

a(0)=1 prepended and a(19)-a(30) from Andrew Howroyd, Apr 14 2021

Status

approved