A238547 Number of partitions p of n such that (number of parts of p) - min(p) is a part of p.

0, 1, 1, 2, 2, 3, 3, 6, 6, 10, 13, 18, 22, 33, 38, 52, 65, 85, 102, 135, 161, 208, 252, 316, 381, 481, 574, 711, 855, 1049, 1252, 1532, 1820, 2207, 2624, 3156, 3740, 4486, 5291, 6308, 7436, 8824, 10363, 12258, 14356, 16912, 19774, 23202, 27056, 31671, 36833

Offset

1,4

Links

Table of n, a(n) for n=1..51.

Formula

a(n) + A238548(n) = A000041(n).

Example

a(6) counts these partitions:  71, 521, 41111.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Length[p]-Min[p]]], {n, 50}]

Prog

(PARI) a(n) = {my(nb = 0); forpart(p=n, if (vecsearch(Vec(p), #p-vecmin(p)), nb++); ); nb; } \\ Michel Marcus, Jun 18 2015

Crossrefs

Cf. A238548.

Sequence in context: A240579 A292225 A238786 * A325681 A116450 A054172

Adjacent sequences: A238544 A238545 A238546 * A238548 A238549 A238550

Keyword

nonn,easy

Author

Clark Kimberling, Feb 28 2014

Status

approved