A284614 Number of partitions of n such that the (sum of distinct odd parts) > n/2.

1, 0, 1, 1, 3, 3, 6, 4, 8, 10, 16, 16, 26, 36, 50, 55, 82, 85, 115, 136, 190, 216, 284, 340, 467, 500, 651, 801, 1066, 1181, 1516, 1665, 2187, 2393, 3050, 3466, 4482, 5028, 6340, 6951, 8895, 9953, 12458, 13640, 17241, 19649, 24385, 26386, 33078, 36138, 44569

Offset

1,5

Links

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

Example

a(5) counts these 3 partitions: 5, 32, 311.

Mathematica

Table[p = IntegerPartitions[n];
 Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], OddQ]], {k, Length[p]}], # > n/2 &]], {n, 55}]

Crossrefs

Cf. A284612, A284613, A284615.

Sequence in context: A182627 A135986 A334848 * A349392 A069734 A265703

Adjacent sequences: A284611 A284612 A284613 * A284615 A284616 A284617

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2017

Status

approved