

A360670


Number of integer partitions of n whose parts have the same mean as their negated first differences.


1



1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 5, 1, 0, 3, 3, 0, 4, 0, 5, 3, 0, 2, 10, 0, 0, 4, 10, 0, 5, 0, 7, 9, 0, 0, 17, 1, 6, 5, 10, 0, 9, 8, 14, 6, 0, 0, 34, 0, 0, 9, 18, 13, 13, 0, 17, 7, 19, 0, 40, 0, 0, 28
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OFFSET

0,13


LINKS



EXAMPLE

The a(n) partitions for n = 4, 12, 24, 27, 30, 44:
(3,1) (9,3) (18,6) (19,7,1) (21,8,1) (33,11)
(9,2,1) (17,6,1) (20,5,2) (22,6,2) (34,5,4,1)
(18,4,2) (21,3,3) (23,4,3) (34,6,3,1)
(19,2,2,1) (25,2,1,1,1) (34,7,2,1)
(19,3,1,1) (34,8,1,1)
(35,4,3,2)
(35,5,2,2)
For example, the partition y = (28,4,3,1), with mean 9, has negated first differences (24,2,1), with mean 9, so y is counted under a(36).


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Mean[#]==Mean[Differences[Reverse[#]]]&]], {n, 0, 30}]


CROSSREFS

These partitions have ranks A360669.
A360614/A360615 = mean of first differences of 0prepended prime indices.


KEYWORD

nonn


AUTHOR



STATUS

approved



