OFFSET
0,4
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.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..1000
EXAMPLE
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)
MATHEMATICA
aug[y_]:=Table[If[i<Length[y], y[[i]]-y[[i+1]]+1, y[[i]]], {i, Length[y]}];
Table[Length[Select[IntegerPartitions[n], OrderedQ[aug[#], Greater]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 01 2019
STATUS
approved