
EXAMPLE

The a(0) = 1 through a(3) = 10 sorted degree sequences:
() (2) (1,1) (1,1,2)
(1,3) (1,1,4)
(2,2) (1,2,3)
(3,3) (1,3,4)
(2,2,2)
(2,2,4)
(2,3,3)
(2,4,4)
(3,3,4)
(4,4,4)
For example, the loopgraphs
{{1,1},{2,2},{3,3},{1,2}}
{{1,1},{2,2},{3,3},{1,3}}
{{1,1},{2,2},{3,3},{2,3}}
{{1,1},{2,2},{1,3},{2,3}}
{{1,1},{3,3},{1,2},{2,3}}
{{2,2},{3,3},{1,2},{1,3}}
all have degrees y = (3,3,2), so y is counted under a(3).


CROSSREFS

See link for additional cross references.
The version without loops is A004251, with covering case A095268.
The halfloop version is A029889, with covering case A339843.
Loopgraphs are counted by A322661 and ranked by A320461 and A340020.
Counting the same partitions by sum gives A339656.
These partitions are ranked by A339658.
The noncovering case (zeros allowed) is A339844.
A007717 counts unlabeled multiset partitions into pairs.
A027187 counts partitions of even length, ranked by A028260.
A058696 counts partitions of even numbers, ranked by A300061.
A101048 counts partitions into semiprimes.
A339655 counts nonloopgraphical partitions of 2n.
A339659 counts graphical partitions of 2n into k parts.
Cf. A001358, A006125, A006129, A062740, A338898, A339841.
Sequence in context: A283070 A222631 A030003 * A234009 A198324 A149175
Adjacent sequences: A339842 A339843 A339844 * A339846 A339847 A339848
