A054952 -id:A054952 - cp's OEIS frontend

A054951 Number of unlabeled semi-strong digraphs on n nodes with mutually nonisomorphic components.

1, 1, 4, 78, 4960, 1041872, 704369984, 1579641879248, 12137443766888448, 328148810741254606592, 31830752699315833628787200, 11234243165959817684710307801600, 14576241398832991116522929933694031872, 70075699209573863790264288901653500497274880

Offset: 1

N. J. A. Sloane, May 24 2000

A digraph is semi-strong if all its weakly connected components are strongly connected. - Andrew Howroyd, Jan 14 2022

V. A. Liskovets, A contribution to the enumeration of strongly connected digraphs, Dokl. AN BSSR, 17 (1973), 1077-1080 (Russian), MR49#4849.

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.

Cf. A035512, A049387, A054952, A054953, A054954.

m = 15;
A035512 = Cases[Import["https://oeis.org/A035512/b035512.txt", "Table"], {, }][[All, 2]];
gf = 1 - Product[(1 - x^n)^A035512[[n + 1]], {n, 1, m}];
CoefficientList[gf + O[x]^m , x] // Rest (* Jean-François Alcover, Aug 26 2019, after Andrew Howroyd *)

G.f.: 1 - Product_{n > 0} (1 - x^n)^A035512(n). - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 11 2003

a(12)-a(14) from Andrew Howroyd, Sep 10 2018

A054953 Number of unlabeled semi-strong digraphs on n nodes with an odd number of pairwise different components.

Original entry on oeis.org

1, 1, 5, 83, 5048, 1047013, 705422455, 1580348377261, 12139024826336632, 328160951350054991463, 31831080872414173375174213, 11234274997368911879051177335450, 14576252633139821208116086572516525403, 70075713785837731364265242597960381223077163

Offset: 1

N. J. A. Sloane, May 24 2000

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.

Cf. A054951, A054952, A054954.

m = 15;
A035512 = Cases[Import["https://oeis.org/A035512/b035512.txt", "Table"], {, }][[All, 2]];
gf = -Product[(1 - x^n)^A035512[[n + 1]], {n, 1, m}] + Product[(1 + x^n)^A035512[[n + 1]], {n, 1, m}];
CoefficientList[gf + O[x]^m , x]/2 // Rest (* Jean-François Alcover, Aug 26 2019, after Andrew Howroyd *)

a(n) = (A054952(n) + A054951(n))/2. - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 11 2003

a(12)-a(14) from Andrew Howroyd, Sep 10 2018

A054954 Number of unlabeled semi-strong digraphs on n nodes with an even number of pairwise different components.

Original entry on oeis.org

0, 0, 1, 5, 88, 5141, 1052471, 706498013, 1581059448184, 12140608800384871, 328173098339746387013, 31831409094194340869533850, 11234306830091593156638822493531, 14576263867574000953696306880725802283

Offset: 1

N. J. A. Sloane, May 24 2000

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.

Cf. A054951, A054952, A054953.

m = 15;
A035512 = Cases[Import["https://oeis.org/A035512/b035512.txt", "Table"], {, }][[All, 2]];
gf = -2 + Product[(1 - x^n)^A035512[[n + 1]], {n, 1, m}] + Product[(1 + x^n)^A035512[[n + 1]], {n, 1, m}];
CoefficientList[gf + O[x]^m , x]/2 // Rest (* Jean-François Alcover, Aug 26 2019, after Andrew Howroyd *)

a(n) = (A054952(n) - A054951(n))/2. - Andrew Howroyd, Sep 10 2018

More terms from Vladeta Jovovic, Mar 11 2003

a(12)-a(14) from Andrew Howroyd, Sep 10 2018

cp's OEIS Frontend

A054951 Number of unlabeled semi-strong digraphs on n nodes with mutually nonisomorphic components.

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A054953 Number of unlabeled semi-strong digraphs on n nodes with an odd number of pairwise different components.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A054954 Number of unlabeled semi-strong digraphs on n nodes with an even number of pairwise different components.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions