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A300788
Number of strict integer partitions of n in which the even parts appear as often at even positions as at odd positions.
12
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 12 2018
EXTENSIONS
a(41)-a(58) from Alois P. Heinz, Mar 13 2018
STATUS
approved