A238544 Number of partitions p of n such that max(p) - (number of parts of p) is a part of p.

0, 0, 0, 1, 0, 2, 1, 4, 3, 7, 6, 14, 12, 23, 24, 39, 41, 66, 71, 106, 120, 168, 193, 268, 306, 411, 482, 629, 737, 953, 1116, 1420, 1675, 2096, 2474, 3076, 3619, 4455, 5257, 6410, 7548, 9157, 10761, 12970, 15238, 18248, 21402, 25531, 29870, 35466, 41452

Offset

1,6

Links

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

Formula

a(n) + A238545(n) = A000041(n).

Example

a(6) counts these partitions:  42, 411.

Mathematica

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

Crossrefs

Cf. A238545.

Sequence in context: A120751 A054082 A339381 * A101708 A339559 A248880

Adjacent sequences: A238541 A238542 A238543 * A238545 A238546 A238547

Keyword

nonn,easy

Author

Clark Kimberling, Feb 28 2014

Status

approved