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

Author

Moshe Shmuel Newman, Jan 10 2011

Keywords

• nonn
• more

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.

Examples

			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.
		

Crossrefs

Cf. A179009, A179822.

Programs

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<Andrew Howroyd, Apr 14 2021

Extensions

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