

A343942


Number of evenlength strict integer partitions of 2n+1.


5



0, 1, 2, 3, 4, 6, 9, 13, 19, 27, 38, 52, 71, 96, 128, 170, 224, 292, 380, 491, 630, 805, 1024, 1295, 1632, 2049, 2560, 3189, 3959, 4896, 6038, 7424, 9100, 11125, 13565, 16496, 20013, 24223, 29249, 35244, 42378, 50849, 60896, 72789, 86841, 103424, 122960, 145937, 172928
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

By conjugation, also the number of integer partitions of 2n+1 covering an initial interval of positive integers with greatest part even.


LINKS



FORMULA



EXAMPLE

The a(1) = 1 through a(7) = 13 strict partitions:
(2,1) (3,2) (4,3) (5,4) (6,5) (7,6) (8,7)
(4,1) (5,2) (6,3) (7,4) (8,5) (9,6)
(6,1) (7,2) (8,3) (9,4) (10,5)
(8,1) (9,2) (10,3) (11,4)
(10,1) (11,2) (12,3)
(5,3,2,1) (12,1) (13,2)
(5,4,3,1) (14,1)
(6,4,2,1) (6,4,3,2)
(7,3,2,1) (6,5,3,1)
(7,4,3,1)
(7,5,2,1)
(8,4,2,1)
(9,3,2,1)


MATHEMATICA

Table[Length[Select[IntegerPartitions[2n+1], UnsameQ@@#&&EvenQ[Length[#]]&]], {n, 0, 15}]


CROSSREFS

The opposite type of strict partition (odd length and even sum) is A344650.
A000041 counts partitions of 2n with alternating sum 0, ranked by A000290.
A103919 counts partitions by sum and alternating sum (reverse: A344612).
A344610 counts partitions by sum and positive reversealternating sum.
Cf. A000070, A000097, A030229, A035294, A067659, A236559, A338907, A343941, A344649, A344654, A344739.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



