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 A054921 Number of connected unlabeled symmetric relations (graphs with loops) having n nodes. 43
 1, 2, 3, 10, 50, 354, 3883, 67994, 2038236, 109141344, 10693855251, 1934271527050, 648399961915988, 404093642681273382, 469756524755173254759, 1022121472711196824292810, 4176802133456105622904206409, 32159648543645931290004658982846 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of non-isomorphic connected antichains of two-element multisets spanning a set of n vertices. Connected antichains are also called clutters. REFERENCES Bender, Edward A., and E. Rodney Canfield. "Enumeration of connected invariant graphs." Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 273. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..86 Edward A. Bender and E. Rodney Canfield, Enumeration of connected invariant graphs, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 273. V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2. FORMULA EULERi transform of A000666. EXAMPLE A000666(n) = Number of increasing sequences of pairs ((x_1,y_1),...,(x_k,y_k)) such that: Sum(x_i)=n and 1<=y_i<=a(x_i+1) for all i. For example the A000666(3)=20 sequences are {((1,1),(1,1),(1,1)), ((1,1),(1,1),(1,2)), ((1,1),(1,2),(1,2)), ((1,2),(1,2),(1,2)); ((1,1),(2,1)), ((1,1),(2,2)), ((1,1),(2,3)), ((1,2),(2,1)), ((1,2),(2,2)), ((1,2),(2,3)); ((3,1)), ((3,2)), ((3,3)), ((3,4)), ((3,5)), ((3,6)), ((3,7)), ((3,8)), ((3,9)), ((3,10))}. - Gus Wiseman, Jul 21 2016 MATHEMATICA nn=8; unlabeledSimpleMluts[n_Integer]:=unlabeledSimpleMluts[n]=Total[Power[2, PermutationCycles[Ordering[Map[Sort, Select[Tuples[Range[n], 2], OrderedQ]/.Table[i->Part[#, i], {i, n}]]], Length]]&/@Permutations[Range[n]]]/n!; multing[t_, n_]:=Array[(t+#-1)/#&, n, 1, Times]; ReplaceAll[a/@Range[0, nn], Solve[Table[unlabeledSimpleMluts[n]==If[n===0, a[0], Total[Function[ptn, Times@@(multing[a[First[#]], Length[#]]&/@Split[ptn])]/@IntegerPartitions[n]]], {n, 0, nn}], a/@Range[0, nn]][[1]]] (* Gus Wiseman, Jul 21 2016 *) CROSSREFS Cf. A000666. Row sums of A304311. Sequence in context: A290713 A020098 A013081 * A192258 A052561 A181927 Adjacent sequences:  A054918 A054919 A054920 * A054922 A054923 A054924 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, May 24 2000 EXTENSIONS More terms from Vladeta Jovovic, Jul 17 2000 Added a(0)=1 by Gus Wiseman, Jul 21 2016 STATUS approved

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Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)