

A325404


Number of reversed integer partitions y of n such that the kth differences of y are distinct for all k >= 0 and are disjoint from the ith differences for i != k.


16



1, 1, 1, 1, 2, 3, 2, 4, 4, 4, 5, 7, 5, 11, 12, 11, 12, 20, 15, 24, 22, 27, 28, 37, 28, 45, 43, 48, 50, 66, 58, 79, 72, 84, 87, 112, 106, 135, 128, 158, 147, 186, 180, 218, 220, 265, 246, 304, 303, 354, 340, 412, 418, 471, 463, 538, 543, 642, 600, 711, 755
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OFFSET

0,5


COMMENTS

The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (3,2).
The zeroth differences of a sequence are the sequence itself, while the kth differences for k > 0 are the differences of the (k1)th differences.
The Heinz numbers of these partitions are given by A325405.


LINKS



EXAMPLE

The a(1) = 1 through a(12) = 5 reversed partitions (A = 10, B = 11, C = 12):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(13) (14) (15) (16) (17) (18) (19) (29) (39)
(23) (25) (26) (27) (28) (38) (57)
(34) (35) (45) (37) (47) (1B)
(46) (56) (2A)
(1A)
(146)


MATHEMATICA

Table[Length[Select[Reverse/@IntegerPartitions[n], UnsameQ@@Join@@Table[Differences[#, k], {k, 0, Length[#]}]&]], {n, 0, 30}]


CROSSREFS

Cf. A279945, A325325, A325349, A325353, A325354, A325365, A325368, A325391, A325393, A325405, A325406, A325468.


KEYWORD

nonn


AUTHOR



STATUS

approved



