cp's OEIS Frontend

A368835 Number of unlabeled n-edge loop-graphs with at most n vertices such that it is not possible to choose a different vertex from each edge.

%I A368835 #13 Jan 14 2024 16:05:22
%S A368835 0,0,0,1,5,23,98,394,1560,6181,24655,99701,410513,1725725,7423757,
%T A368835 32729320,148027044,687188969,3275077017,16022239940,80431483586,
%U A368835 414094461610,2185052929580,11808696690600,65312048149993,369408792148714,2135111662435080,12601466371445619
%N A368835 Number of unlabeled n-edge loop-graphs with at most n vertices such that it is not possible to choose a different vertex from each edge.
%H A368835 Andrew Howroyd, <a href="/A368835/b368835.txt">Table of n, a(n) for n = 0..50</a>
%F A368835 a(n) = A368598(n) - A368984(n). - _Andrew Howroyd_, Jan 14 2024
%e A368835 Non-isomorphic representatives of the a(4) = 5 loop-graphs:
%e A368835   {{1,1},{2,2},{3,3},{1,2}}
%e A368835   {{1,1},{2,2},{1,2},{1,3}}
%e A368835   {{1,1},{2,2},{1,2},{3,4}}
%e A368835   {{1,1},{2,2},{1,3},{2,3}}
%e A368835   {{1,1},{1,2},{1,3},{2,3}}
%t A368835 Table[Length[Union[sysnorm /@ Select[Subsets[Subsets[Range[n],{1,2}],{n}],Select[Tuples[#], UnsameQ@@#&]=={}&]]],{n,0,5}]
%Y A368835 The case of a unique choice is A000081, row sums of A106234.
%Y A368835 The labeled version is A368596, covering A368730.
%Y A368835 Without the choice condition we have A368598.
%Y A368835 The complement is A368984, row sums of A368926.
%Y A368835 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A368835 A006125 counts graphs, unlabeled A000088.
%Y A368835 A006129 counts covering graphs, unlabeled A002494.
%Y A368835 A014068 counts loop-graphs, unlabeled A000666.
%Y A368835 A058891 counts set-systems (without singletons A016031), unlabeled A000612.
%Y A368835 A322661 counts labeled covering half-loop-graphs, connected A062740.
%Y A368835 Cf. A116508, A129271, A133686, A137916, A137917, A333331, A367863, A368836, A368924, A368927.
%K A368835 nonn
%O A368835 0,5
%A A368835 _Gus Wiseman_, Jan 13 2024
%E A368835 a(8) onwards from _Andrew Howroyd_, Jan 14 2024