A370169 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A370169

Number of unlabeled loop-graphs covering n vertices with at most n edges.

1, 1, 3, 7, 19, 48, 135, 373, 1085, 3184, 9590, 29258, 90833, 285352, 908006, 2919953, 9487330, 31111997, 102934602, 343389708, 1154684849, 3912345408, 13353796977, 45906197103, 158915480378, 553897148543, 1943627750652, 6865605601382, 24411508473314, 87364180212671, 314682145679491 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	LINKS	`Andrew Howroyd, Table of n, a(n) for n = 0..50`
	EXAMPLE	`The a(0) = 1 through a(4) = 19 loop-graph edge sets (loops shown as singletons):` `{} {{1}} {{1,2}} {{1},{2,3}} {{1,2},{3,4}}` `{{1},{2}} {{1,2},{1,3}} {{1},{2},{3,4}}` `{{1},{1,2}} {{1},{2},{3}} {{1},{1,2},{3,4}}` `{{1},{2},{1,3}} {{1},{2,3},{2,4}}` `{{1},{1,2},{1,3}} {{1},{2},{3},{4}}` `{{1},{1,2},{2,3}} {{1,2},{1,3},{1,4}}` `{{1,2},{1,3},{2,3}} {{1,2},{1,3},{2,4}}` `{{1},{2},{3},{1,4}}` `{{1},{2},{1,2},{3,4}}` `{{1},{2},{1,3},{1,4}}` `{{1},{2},{1,3},{2,4}}` `{{1},{2},{1,3},{3,4}}` `{{1},{1,2},{1,3},{1,4}}` `{{1},{1,2},{1,3},{2,4}}` `{{1},{1,2},{2,3},{2,4}}` `{{1},{1,2},{2,3},{3,4}}` `{{1},{2,3},{2,4},{3,4}}` `{{1,2},{1,3},{1,4},{2,3}}` `{{1,2},{1,3},{2,4},{3,4}}`
	MATHEMATICA	`brute[m_]:=First[Sort[Table[Sort[Sort /@ (m/.Rule@@@Table[{(Union@@m)[[i]], p[[i]]}, {i, Length[p]}])], {p, Permutations[Range[Length[Union@@m]]]}]]];` `Table[Length[Union[brute /@ Select[Subsets[Subsets[Range[n], {1, 2}]], Union@@#==Range[n]&&Length[#]<=n&]]], {n, 0, 5}]`
	PROG	`(PARI) \\ G defined in A070166.` `a(n)=my(A=O(x*x^n)); if(n==0, 1, polcoef((G(n, A)-G(n-1, A))/(1-x), n)) \\ Andrew Howroyd, Feb 19 2024`
	CROSSREFS	`The case of equality is A368599, covering case of A368598.` `The labeled version is A369194, covering case of A066383.` `This is the covering case of A370168.` `The loopless version is the covering case of A370315, labeled A369192.` `This is the loopless version is A370316, labeled A369191.` `A006125 counts graphs, unlabeled A000088.` `A006129 counts covering graphs, unlabeled A002494.` `A322661 counts covering loop-graphs, unlabeled A322700.` `Cf. A000666, A005703, A014068, A062740, A116508, A368597, A368927, A369141, A369196, A369197, A369199.` `Sequence in context: A246493 A293733 A073063 * A007288 A191824 A191757` `Adjacent sequences: A370166 A370167 A370168 * A370170 A370171 A370172`
	KEYWORD	`nonn`
	AUTHOR	`Gus Wiseman, Feb 16 2024`
	EXTENSIONS	`a(7) onwards from Andrew Howroyd, Feb 19 2024`
	STATUS	`approved`

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 28 23:11 EDT 2024. Contains 375508 sequences. (Running on oeis4.)