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A054920 Number of connected unlabeled reflexive relations with n nodes such that complement is also connected. 1
2, 4, 68, 2592, 278796, 95720106, 111891292036, 457846756500066, 6664787020904248568, 349363873490889302878250, 66602024342830108271942323060, 46557190064705399729526041154647820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

FORMULA

a(n) = 2*A054919(n) - A000595(n).

MATHEMATICA

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

A000595 = Import["https://oeis.org/A000595/b000595.txt", "Table"][[All, 2]];

A054919 = Join[{1}, EULERi[A000595 // Rest]];

a[n_] := 2*A054919[[n + 1]] - A000595[[n + 1]];

Array[a, 50] (* Jean-Fran├žois Alcover, Sep 01 2019 *)

CROSSREFS

Cf. A000595, A054919.

Sequence in context: A018364 A100603 A301818 * A062061 A066974 A270583

Adjacent sequences:  A054917 A054918 A054919 * A054921 A054922 A054923

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 24 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jul 17 2000

STATUS

approved

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Last modified October 17 21:16 EDT 2019. Contains 328132 sequences. (Running on oeis4.)