A300787 Number of integer partitions of n in which the even parts appear as often at even positions as at odd positions.

1, 1, 1, 2, 3, 4, 6, 8, 12, 15, 21, 27, 38, 47, 63, 79, 106, 130, 170, 209, 272, 330, 422, 512, 653, 784, 986, 1183, 1482, 1765, 2191, 2604, 3218, 3804, 4666, 5504, 6726, 7898, 9592, 11240, 13602, 15880, 19122, 22277, 26733, 31048, 37102, 43003, 51232, 59220

Offset

0,4

Links

Table of n, a(n) for n=0..49.

Example

The a(7) = 8 partitions: (7), (511), (421), (331), (322), (31111), (22111), (1111111). Missing are: (61), (52), (43), (4111), (3211), (2221), (211111).

Mathematica

cobal[y_]:=Sum[(-1)^x, {x, Join@@Position[y, _?EvenQ]}];
Table[Length[Select[IntegerPartitions[n], cobal[#]===0&]], {n, 0, 50}]

Crossrefs

Even- and odd-indexed terms are A006330 and A001523 respectively, which add up to A000712.

Cf. A000898, A001405, A026010, A045931, A058696, A063886, A097613, A130780, A171966, A239241, A300788, A300789.

Sequence in context: A178751 A309353 A081029 * A171966 A034893 A187448

Adjacent sequences: A300784 A300785 A300786 * A300788 A300789 A300790

Keyword

nonn

Author

Gus Wiseman, Mar 12 2018

Status

approved