cp's OEIS Frontend

A369142 Number of labeled loop-graphs covering {1..n} such that it is not possible to choose a different vertex from each edge (non-choosable).

%I A369142 #10 Feb 02 2024 18:35:31
%S A369142 0,0,1,22,616,26084,1885323,253923163,66619551326,34575180977552,
%T A369142 35680008747431929,73392583275070667841,301348381377662031986734,
%U A369142 2471956814761854578316988092,40530184362443276558060719358471,1328619783326799871747200601484790193
%N A369142 Number of labeled loop-graphs covering {1..n} such that it is not possible to choose a different vertex from each edge (non-choosable).
%C A369142 Also labeled loop-graphs covering n vertices with at least one connected component containing more edges than vertices.
%H A369142 Andrew Howroyd, <a href="/A369142/b369142.txt">Table of n, a(n) for n = 0..50</a>
%F A369142 Inverse binomial transform of A369141.
%F A369142 a(n) = A322661(n) - A369140(n). - _Andrew Howroyd_, Feb 02 2024
%e A369142 The a(0) = 0 through a(3) = 22 loop-graphs (loops shown as singletons):
%e A369142   .  .  {{1},{2},{1,2}}  {{1},{2},{3},{1,2}}
%e A369142                          {{1},{2},{3},{1,3}}
%e A369142                          {{1},{2},{3},{2,3}}
%e A369142                          {{1},{2},{1,2},{1,3}}
%e A369142                          {{1},{2},{1,2},{2,3}}
%e A369142                          {{1},{2},{1,3},{2,3}}
%e A369142                          {{1},{3},{1,2},{1,3}}
%e A369142                          {{1},{3},{1,2},{2,3}}
%e A369142                          {{1},{3},{1,3},{2,3}}
%e A369142                          {{2},{3},{1,2},{1,3}}
%e A369142                          {{2},{3},{1,2},{2,3}}
%e A369142                          {{2},{3},{1,3},{2,3}}
%e A369142                          {{1},{1,2},{1,3},{2,3}}
%e A369142                          {{2},{1,2},{1,3},{2,3}}
%e A369142                          {{3},{1,2},{1,3},{2,3}}
%e A369142                          {{1},{2},{3},{1,2},{1,3}}
%e A369142                          {{1},{2},{3},{1,2},{2,3}}
%e A369142                          {{1},{2},{3},{1,3},{2,3}}
%e A369142                          {{1},{2},{1,2},{1,3},{2,3}}
%e A369142                          {{1},{3},{1,2},{1,3},{2,3}}
%e A369142                          {{2},{3},{1,2},{1,3},{2,3}}
%e A369142                          {{1},{2},{3},{1,2},{1,3},{2,3}}
%t A369142 Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]],Union@@#==Range[n]&&Length[Select[Tuples[#],UnsameQ@@#&]]==0&]],{n,0,5}]
%Y A369142 The version for a unique choice is A000272, unlabeled A000055.
%Y A369142 Without the choice condition we have A006125, unlabeled A000088.
%Y A369142 The case without loops is A367868, covering case of A367867.
%Y A369142 For exactly n edges we have A368730, covering case of A368596.
%Y A369142 The complement is counted by A369140, covering case of A368927.
%Y A369142 This is the covering case of A369141.
%Y A369142 For n edges and no loops we have A369144, covering A369143.
%Y A369142 The unlabeled version is A369147, covering case of A369146.
%Y A369142 A000085, A100861, A111924 count set partitions into singletons or pairs.
%Y A369142 A006129 counts covering graphs, unlabeled A002494.
%Y A369142 A054548 counts graphs covering n vertices with k edges, with loops A369199.
%Y A369142 A129271 counts connected choosable graphs, unlabeled A005703.
%Y A369142 A133686 counts choosable graphs, covering A367869.
%Y A369142 A322661 counts covering loop-graphs, connected A062740, unlabeled A322700.
%Y A369142 A367902 counts choosable set-systems, complement A367903.
%Y A369142 Cf. A000666, A003465, A006649, A116508, A137916, A333331, A368600, A368924, A368984, A369145, A369194.
%K A369142 nonn
%O A369142 0,4
%A A369142 _Gus Wiseman_, Jan 20 2024
%E A369142 a(6) onwards from _Andrew Howroyd_, Feb 02 2024