

A238628


Number of partitions p of n such that n  max(p) is a part of p.


27



0, 1, 1, 3, 2, 5, 3, 8, 4, 11, 5, 16, 6, 21, 7, 29, 8, 38, 9, 51, 10, 66, 11, 88, 12, 113, 13, 148, 14, 190, 15, 246, 16, 313, 17, 402, 18, 508, 19, 646, 20, 812, 21, 1023, 22, 1277, 23, 1598, 24, 1982, 25, 2461, 26, 3036, 27, 3745, 28, 4593, 29, 5633
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

Also the number of integer partitions of n that are of length 2 or contain n/2. The first condition alone is A004526, complement A058984. The second condition alone is A035363, complement A086543, ranks A344415.  Gus Wiseman, Oct 07 2023


LINKS



EXAMPLE

a(6) counts these partitions: 51, 42, 33, 321, 3111.


MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, n  Max[p]]], {n, 50}]


PROG

(Python)
from sympy.utilities.iterables import partitions
def A238628(n): return sum(1 for p in partitions(n) if nmax(p, default=0) in p) # Chai Wah Wu, Sep 21 2023
(PARI) a(n) = my(res = floor(n/2)); if(!bitand(n, 1), res+=(numbpart(n/2)1)); res


CROSSREFS

The complement is counted by A365825.
These partitions are ranked by A366318.
A182616 counts partitions of 2n that do not contain n, strict A365828.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



