A238628 - OEIS

A238628

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

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

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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

Table of n, a(n) for n=1..60.

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 n-max(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