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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. 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 (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 June 6 06:26 EDT 2023. Contains 363139 sequences. (Running on oeis4.)