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A325324 Number of integer partitions of n whose differences (with the last part taken to be 0) are distinct.

%I A325324 #19 Feb 27 2021 12:06:47
%S A325324 1,1,2,1,3,4,4,7,7,7,10,15,13,22,25,26,31,43,39,55,54,68,75,98,97,128,
%T A325324 135,165,177,217,223,277,282,339,356,438,444,527,553,667,694,816,868,
%U A325324 1015,1054,1279,1304,1538,1631,1849,1958,2304,2360,2701,2899,3267
%N A325324 Number of integer partitions of n whose differences (with the last part taken to be 0) are distinct.
%C A325324 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) (with the last part taken to be 0) are (-3,-2,-1).
%C A325324 The Heinz numbers of these partitions are given by A325367.
%H A325324 Fausto A. C. Cariboni, <a href="/A325324/b325324.txt">Table of n, a(n) for n = 0..400</a>
%H A325324 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>.
%e A325324 The a(1) = 1 through a(11) = 15 partitions (A = 10, B = 11):
%e A325324   (1)  (2)   (3)  (4)   (5)    (6)    (7)    (8)    (9)    (A)    (B)
%e A325324        (11)       (22)  (32)   (33)   (43)   (44)   (54)   (55)   (65)
%e A325324                   (31)  (41)   (51)   (52)   (53)   (72)   (64)   (74)
%e A325324                         (311)  (411)  (61)   (62)   (81)   (73)   (83)
%e A325324                                       (322)  (71)   (441)  (82)   (92)
%e A325324                                       (331)  (332)  (522)  (91)   (A1)
%e A325324                                       (511)  (611)  (711)  (433)  (443)
%e A325324                                                            (622)  (533)
%e A325324                                                            (631)  (551)
%e A325324                                                            (811)  (632)
%e A325324                                                                   (641)
%e A325324                                                                   (722)
%e A325324                                                                   (731)
%e A325324                                                                   (911)
%e A325324                                                                   (6311)
%e A325324 For example, (6,3,1,1) has differences (-3,-2,0,-1), which are distinct, so (6,3,1,1) is counted under a(11).
%t A325324 Table[Length[Select[IntegerPartitions[n],UnsameQ@@Differences[Append[#,0]]&]],{n,0,30}]
%Y A325324 Cf. A007862, A049988, A098859, A130091, A240026, A320348, A320466, A320509, A325325, A325349, A325366, A325367, A325368, A325404, A325407.
%K A325324 nonn
%O A325324 0,3
%A A325324 _Gus Wiseman_, Apr 23 2019