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A367588
Number of integer partitions of n with exactly two distinct parts, both appearing with the same multiplicity.
4
0, 0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 5, 9, 6, 9, 10, 11, 8, 15, 9, 16, 14, 15, 11, 23, 14, 18, 18, 23, 14, 30, 15, 26, 22, 24, 22, 38, 18, 27, 26, 38, 20, 42, 21, 37, 36, 33, 23, 53, 27, 42, 34, 44, 26, 54, 34, 53, 38, 42, 29, 74, 30, 45, 49, 57, 40, 66, 33, 58, 46
OFFSET
0,6
COMMENTS
The Heinz numbers of these partitions are given by A268390.
LINKS
FORMULA
G.f.: Sum_{i, j>0} x^(j*(2*i+1))/(1-x^j). - John Tyler Rascoe, Feb 04 2024
EXAMPLE
The a(3) = 1 through a(12) = 9 partitions (A = 10, B = 11):
(21) (31) (32) (42) (43) (53) (54) (64) (65) (75)
(41) (51) (52) (62) (63) (73) (74) (84)
(2211) (61) (71) (72) (82) (83) (93)
(3311) (81) (91) (92) (A2)
(222111) (3322) (A1) (B1)
(4411) (4422)
(5511)
(333111)
(22221111)
MATHEMATICA
Table[Sum[Floor[(d-1)/2], {d, Divisors[n]}], {n, 30}]
CROSSREFS
For any multiplicities we have A002133, ranks A007774.
For any number of distinct parts we have A047966, ranks A072774.
For distinct multiplicities we have A182473, ranks A367589.
These partitions have ranks A268390.
A000041 counts integer partitions, strict A000009.
A072233 counts partitions by number of parts.
A116608 counts partitions by number of distinct parts.
Sequence in context: A332682 A304183 A157222 * A320033 A333527 A064047
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 01 2023
STATUS
approved