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A325404 Number of reversed integer partitions y of n such that the k-th differences of y are distinct for all k >= 0 and are disjoint from the i-th differences for i != k. 15
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 (list; graph; refs; listen; history; text; internal format)
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 k-th differences for k > 0 are the differences of the (k-1)-th differences.

The Heinz numbers of these partitions are given by A325405.

LINKS

Table of n, a(n) for n=0..60.

Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

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.

Sequence in context: A081315 A035662 A249870 * A324750 A320348 A336315

Adjacent sequences:  A325401 A325402 A325403 * A325405 A325406 A325407

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 02 2019

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)