OFFSET
1,2
COMMENTS
The decapitation of such a partition (delete the greatest part) is term-wise greater than or equal to its negated first-differences.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 1..250
EXAMPLE
The a(1) = 1 through a(8) = 13 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (43) (44)
(111) (211) (221) (42) (322) (53)
(1111) (2111) (222) (421) (332)
(11111) (321) (2221) (422)
(2211) (3211) (2222)
(21111) (22111) (3221)
(111111) (211111) (4211)
(1111111) (22211)
(32111)
(221111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@Thread[Differences[-#]<=Rest[#]]&]], {n, 30}]
CROSSREFS
The version with no adjacent parts having quotient < 2 is A000929.
The case of equality (all adjacent parts having quotient 2) is A154402.
The strict case is A342095.
The version with all adjacent parts having quotient > 2 is A342098.
The Heinz numbers of these partitions are listed by A342191.
A000009 counts strict partitions.
A003114 counts partitions with adjacent parts differing by more than 1.
A034296 counts partitions with adjacent parts differing by at most 1.
A161908 lists superior prime divisors.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 02 2021
STATUS
approved