A300788 Number of strict integer partitions of n in which the even parts appear as often at even positions as at odd positions.

1, 1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 19, 23, 26, 30, 35, 42, 47, 54, 62, 73, 82, 94, 107, 124, 139, 158, 179, 206, 230, 260, 293, 334, 372, 420, 470, 532, 591, 664, 740, 835, 924, 1034, 1148, 1288, 1422, 1588, 1756, 1962, 2161, 2404

Offset: 0

Author

Gus Wiseman, Mar 12 2018

Keywords

• nonn

Examples

			The a(9) = 3 strict partitions: (9), (621), (531). Missing are: (81), (72), (63), (54), (432).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4000 (first 291 terms from Fausto A. C. Cariboni)

Crossrefs

Cf. A000712, A000898, A001405, A026010, A045931, A063886, A097613, A130780, A171966, A239241, A300787, A300789.

Programs

Mathematica

cobal[y_]:=Sum[(-1)^x,{x,Join@@Position[y,_?EvenQ]}];
Table[Length[Select[IntegerPartitions[n],cobal[#]===0&&UnsameQ@@#&]],{n,0,40}]

Extensions

a(41)-a(58) from Alois P. Heinz, Mar 13 2018