A000250 Number of symmetric reflexive relations on n nodes: (1/2)*A000666. (Formerly M2868 N1153)

1, 3, 10, 45, 272, 2548, 39632, 1104306, 56871880, 5463113568, 978181717680, 326167542296048, 202701136710498400, 235284321080559981952, 511531711735594715527360, 2089424601541011618029114896, 16084004145036771186002041099712, 234026948449058790311618594954430848, 6454432593140577452393525511509194184320

Offset

1,2

References

Harary, Frank; Palmer, Edgar M.; Robinson, Robert W.; Schwenk, Allen J.; Enumeration of graphs with signed points and lines. J. Graph Theory 1 (1977), no. 4, 295-308.

M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sept. 15, 1955, pp. 14-22.

W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Jean-François Alcover, Table of n, a(n) for n = 1..40

M. D. McIlroy, Calculation of numbers of structures of relations on finite sets, Massachusetts Institute of Technology, Research Laboratory of Electronics, Quarterly Progress Reports, No. 17, Sep. 15, 1955, pp. 14-22. [Annotated scanned copy]

Mathematica

permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
edges[v_] := Sum[Sum[GCD[v[[i]], v[[j]]], {j, 1, i - 1}], {i, 2, Length[v]} ] + Sum[Quotient[v[[i]], 2] + 1, {i, 1, Length[v]}];
a[n_] := Module[{s = 0}, Do[s += permcount[p]*2^edges[p], {p, IntegerPartitions[n]}]; s/(2  n!)];
a /@ Range[19] (* Jean-François Alcover, Jan 17 2020, after Andrew Howroyd in A000666 *)

Crossrefs

Cf. A000595, A001173, A001174.

Sequence in context: A292181 A236409 A348468 * A118601 A005143 A356572

Adjacent sequences: A000247 A000248 A000249 * A000251 A000252 A000253

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 18 2000

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007

Status

approved