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

0,7

Links

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A096911 A143752 A145933 * A120171 A364915 A145816

Adjacent sequences: A300785 A300786 A300787 * A300789 A300790 A300791

Keyword

nonn

Author

Gus Wiseman, Mar 12 2018

Extensions

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

Status

approved