OFFSET
0,3
COMMENTS
For the definition, see sequence A179009. This sequence counts the same objects using a different statistic, the largest part rather than the sum of the parts.
a(n) is the number of subsets of {1..n-1} containing the sum of any two distinct elements whose sum is <= n. This differs from A326080 in that the set may not contain n itself. These sets are the complements of the set of parts in the first definition. - Andrew Howroyd, Apr 13 2021
EXAMPLE
The partitions counted by n=4 are:
4+1, 4+2+1, 4+3+1, 4+3+2, 4+3+2+1.
The partitions counted by n=5 are:
5+2+1, 5+3+1, 5+3+2+1, 5+4+2+1, 5+4+3+1, 5+4+3+2, 5+4+3+2+1.
PROG
(PARI)
a(n)={
my(ok(k, b)=for(i=1, (k-1)\2, if(bittest(b, i) && bittest(b, k-i), return(0))); 1);
my(recurse(k, b)=if(k==n, ok(k, b), self()(k+1, bitor(b, 1<<k)) + if(ok(k, b), self()(k+1, b))));
if(n<1, n==0, recurse(1, 0))
} \\ Andrew Howroyd, Apr 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Moshe Shmuel Newman, Jan 10 2011
EXTENSIONS
a(19)-a(42) from Andrew Howroyd, Apr 13 2021
STATUS
approved