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.
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
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