OFFSET
1,5
COMMENTS
Also, the number of partitions of n such that (greatest part) >= 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) <= 0.
Also, the number of partitions p of n such that max(max(p), 2*(number of parts of p)) is a part of p.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
EXAMPLE
The partitions of 6 that do not qualify are 22311, 21111, 111111, so that a(6) = 11 - 3 = 8.
MATHEMATICA
z = 50; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] <= Length[p]], {n, z}]
(* also *)
Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[Max[p], 2*Length[p]]]], {n, 50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 13 2014
STATUS
approved