A325358 Number of integer partitions of n whose augmented differences are strictly decreasing.

1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 6, 7, 9, 10, 11, 13, 14, 15, 18, 20, 21, 24, 26, 28, 33, 36, 38, 43, 46, 49, 56, 60, 63, 71, 76, 80, 90, 96, 100, 112, 120, 125, 139, 149, 155, 171, 183, 190, 208, 223, 232, 252, 269, 280, 304, 325, 338, 364, 387, 403

Offset: 0

Author

Gus Wiseman, May 01 2019

Keywords

• nonn

Comments

The augmented differences aug(y) of an integer partition y of length k are given by aug(y)i = y_i - y{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3).

The Heinz numbers of these partitions are given by A325396.

Examples

			The a(1) = 1 through a(11) = 6 partitions:
  (1)  (2)  (3)   (4)   (5)   (6)   (7)    (8)    (9)    (10)   (11)
            (21)  (31)  (41)  (42)  (52)   (62)   (63)   (73)   (83)
                              (51)  (61)   (71)   (72)   (82)   (92)
                                    (421)  (521)  (81)   (91)   (101)
                                                  (621)  (631)  (731)
                                                         (721)  (821)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..1000
• Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts.

Crossrefs

Cf. A049988, A240026, A320466, A325349, A325350, A325351, A325356, A325357, A325359, A325393.

Programs

Mathematica

aug[y_]:=Table[If[i