A054919 -id:A054919

Search: a054919 -id:a054919

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A318590

Number of connected balanced signed graphs on n unlabeled nodes.

+10
3

1, 1, 2, 5, 28, 177, 1982, 33997, 1020516, 54570672, 5347070228, 967135763525, 324200029119318, 202046821340636691, 234878262433630160622, 511060736355598412146405, 2088401066728281847415734793, 16079824271822965645002329491423, 233994776259866281916838227225733732

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

Wikipedia, Signed graph

FORMULA

a(2*n+1) = A054921(2*n+1)/2, a(2*n) = (a(n) + A054919(n) + A054921(2*n) - A054921(n))/2.

Inverse Euler transform of A034892.

CROSSREFS

Cf. A005142, A034892, A053465, A054919, A054921.

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Sep 25 2018

STATUS

approved

A054920

Number of connected unlabeled reflexive relations with n nodes such that complement is also connected.

+10
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

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

(* EulerInvTransform is defined in A022562 *)

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

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

Array[a, 50] (* Jean-François Alcover, Sep 01 2019, updated Mar 17 2020 *)

CROSSREFS

Cf. A000595, A054919.

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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