A325357 Number of integer partitions of n whose augmented differences are strictly increasing.

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 3, 5, 5, 4, 5, 6, 5, 7, 7, 7, 7, 9, 7, 10, 10, 8, 11, 13, 10, 13, 14, 12, 14, 17, 13, 17, 19, 17, 18, 22, 19, 22, 24, 21, 24, 28, 24, 29, 30, 28, 31, 35, 30, 35, 40, 36

Offset: 0

Author

Gus Wiseman, Apr 23 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 A325395.

Examples

			The a(28) = 10 partitions:
  (28)
  (18,10)
  (17,11)
  (16,12)
  (15,13)
  (14,14)
  (12,10,6)
  (11,10,7)
  (10,10,8)
  (8,8,7,5)
For example, the augmented differences of (8,8,7,5) are (1,2,3,5), which are strictly increasing.
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000837, A007294, A049988, A098859, A325351, A325356, A325360, A325391, A325395.

Programs

Mathematica

aug[y_]:=Table[If[i