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

Author

Gus Wiseman, Mar 12 2018

Keywords

• nonn

Examples

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

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.

Programs

Mathematica

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