A238548 Number of partitions p of n such that (number of parts of p) - min(p) is not a part of p.

1, 1, 2, 3, 5, 8, 12, 16, 24, 32, 43, 59, 79, 102, 138, 179, 232, 300, 388, 492, 631, 794, 1003, 1259, 1577, 1955, 2436, 3007, 3710, 4555, 5590, 6817, 8323, 10103, 12259, 14821, 17897, 21529, 25894, 31030, 37147, 44350, 52898, 62917, 74778, 88646, 104980

Offset

1,3

Links

Table of n, a(n) for n=1..47.

Formula

a(n) + A238547(n) = A000041(n).

Example

a(6) = 8 counts all 11 partitions of 6 except these:  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. A238547.

Sequence in context: A305377 A062489 A084624 * A356235 A004170 A247116

Adjacent sequences: A238545 A238546 A238547 * A238549 A238550 A238551

Keyword

nonn,easy

Author

Clark Kimberling, Feb 28 2014

Status

approved