cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A350906 Number of unlabeled initially-finally connected digraphs with n arcs.

Original entry on oeis.org

1, 1, 2, 5, 16, 56, 241, 1111, 5748, 31912, 190328, 1204317, 8050341, 56516303, 415128256, 3179020729, 25308005049, 208918893640, 1784451646305, 15739926014382, 143130061546156, 1339761466105929, 12891329514544223, 127351374611721837, 1290198076415425548, 13390893744153374776
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A057278.
Cf. A049531 (by vertices), A350752, A350796, A350798, A350907.

Programs

A350907 Number of unlabeled initially connected digraphs with n arcs.

Original entry on oeis.org

1, 1, 3, 8, 29, 111, 522, 2604, 14459, 85796, 544753, 3659313, 25902251, 192171887, 1489090036, 12011329453, 100583184087, 872346402439, 7819597099285, 72313198682817, 688784601395670, 6747614973580663, 67896777481378196, 700913648767703716, 7415270780191604414, 80316990564932960558
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A057277.
Cf. A051421 (by vertices), A350752, A350796, A350798, A350906.

Programs

A361582 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k strongly connected components.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 0, 5, 5, 6, 0, 83, 62, 42, 31, 0, 5048, 2494, 1172, 592, 302, 0, 1047008, 330063, 103961, 38312, 15616, 5984, 0, 705422362, 137934757, 28095923, 7243110, 2297690, 795930, 243668, 0, 1580348371788, 184557780045, 23226116293, 3951426731, 914429926, 261269562, 79512478, 20286025
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Examples

			Triangle begins:
  1;
  0,       1;
  0,       1,      2;
  0,       5,      5,      6;
  0,      83,     62,     42,    31;
  0,    5048,   2494,   1172,   592,   302;
  0, 1047008, 330063, 103961, 38312, 15616, 5984;
  ...

Links

Crossrefs

Column k=1 is A035512.
Main diagonal is A003087.
Row sums are A000273.
The labeled version is A361455.
Cf. A106238, A350794, A361587, A361588.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A361582triang(6)); for(n=1, #A, print(A[n])) }

A361588 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k strongly connected components and without isolated nodes.

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 5, 4, 4, 0, 83, 57, 37, 25, 0, 5048, 2411, 1110, 550, 271, 0, 1047008, 325015, 101467, 37140, 15024, 5682, 0, 705422362, 136887749, 27765860, 7139149, 2259378, 780314, 237684, 0, 1580348371788, 183852357683, 23088181536, 3923330808, 907186816, 258971872, 78716548, 20042357
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Examples

			Triangle begins:
  1;
  0,       0;
  0,       1,      1;
  0,       5,      4,      4;
  0,      83,     57,     37,    25;
  0,    5048,   2411,   1110,   550,   271;
  0, 1047008, 325015, 101467, 37140, 15024, 5682;
  ...

Crossrefs

Column k=1 is A035512.
Main diagonal is A361589.
Row sums are A053598.
Cf. A350794, A361582, A361587, A361590.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A361588triang(6)); for(n=1, #A, print(A[n])) }

Formula

T(n,k) = A361582(n,k) - A361582(n-1,k-1).

A049387 Number of rooted unlabeled strongly connected digraphs with n nodes.

Original entry on oeis.org

1, 1, 10, 287, 24427, 6222400, 4924590115, 12632686344657, 109225745061589342, 3281390460782419035867, 350135321051253376431022071, 134810599506208376766503740475912, 189491014587142646710566991248361106383, 981059614010249061197621212287544752507380541
Offset: 1

Views

Author

Valery A. Liskovets

Keywords

Comments

There is a rather difficult formula (simplified in 1973). The subsequent published value 6222928 for n=6 needs to be verified.
The correct value is 6222400. Terms up to a(7) have been confirmed by brute force using digraphs generated by nauty. - Andrew Howroyd, Jan 12 2022

Links

Crossrefs

Cf. A035512, A350794.

Programs

Extensions

Terms a(6) and beyond from Andrew Howroyd, Jan 12 2022

A361586 Number of digraphs on n unlabeled nodes in which every node belongs to a directed cycle.

Original entry on oeis.org

1, 0, 1, 5, 90, 5289, 1071691, 712342075, 1585944117738, 12152982231404393, 328276896613548366675, 31834464336872565979301363, 11234630426387288679040317490771, 14576388456695908232721134339830232699, 70075904005979773819582865772534172929477101
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Crossrefs

Column k=0 of A361590.
The labeled version is A086366.
Cf. A350794.

Programs

A361587 Triangle read by rows: T(n,k) is the number of weakly connected digraphs on n unlabeled nodes with k strongly connected components.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 5, 4, 4, 0, 83, 56, 36, 24, 0, 5048, 2406, 1101, 542, 267, 0, 1047008, 324917, 101307, 37017, 14947, 5647, 0, 705422362, 136882286, 27757789, 7134897, 2257234, 779257, 237317, 0, 1580348371788, 183851281949, 23086772643, 3922864504, 907027520, 258909828, 78691767, 20035307
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Examples

			Triangle begins:
  1;
  0,       1;
  0,       1,      1;
  0,       5,      4,      4;
  0,      83,     56,     36,    24;
  0,    5048,   2406,   1101,   542,   267;
  0, 1047008, 324917, 101307, 37017, 14947, 5647;
  ...

Crossrefs

Column k=1 is A035512.
Main diagonal is A101228.
Row sums are A003085.
Cf. A350794, A361582, A361588.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A361587triang(6)); for(n=1, #A, print(A[n])) }

A361590 Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with exactly k strongly connected components of size 1.

Original entry on oeis.org

1, 0, 1, 1, 0, 2, 5, 5, 0, 6, 90, 55, 42, 0, 31, 5289, 2451, 974, 592, 0, 302, 1071691, 323709, 94332, 29612, 15616, 0, 5984, 712342075, 135208025, 25734232, 6059018, 1650492, 795930, 0, 243668, 1585944117738, 181427072519, 21650983294, 3358042412, 704602272, 174576110, 79512478, 0, 20286025
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Examples

			Triangle begins:
        1;
        0,      1;
        1,      0,     2;
        5,      5,     0,     6;
       90,     55,    42,     0,    31;
     5289,   2451,   974,   592,     0, 302;
  1071691, 323709, 94332, 29612, 15616,   0, 5984;
  ...

Crossrefs

Column k=0 is A361586.
Main diagonal is A003087.
Row sums are A000273.
The labeled version is A361592.
Cf. A350794, A361582, A361588.

Programs

  • PARI
    \\ See PARI link in A350794 for program code.
{ my(A=A361590triang(6)); for(n=1, #A, print(A[n])) }

A361583 Number of digraphs on n unlabeled nodes whose strongly connected components are complete digraphs.

Original entry on oeis.org

1, 1, 3, 12, 88, 1217, 34672, 2039085, 246005109, 60296886108, 29828186693218, 29663937774464786, 59172529527454608139, 236453014376786629601848, 1891427400988740573006253862, 30274661556583530830890359188257, 969429810937979825934973090455224882
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Crossrefs

The labeled version is A361560.
Cf. A000273, A350794, A361584, A361585.

Programs

A361584 Number of digraphs on n unlabeled nodes whose strongly connected components are directed cycles or single vertices.

Original entry on oeis.org

1, 1, 3, 12, 88, 1239, 36540, 2226595, 277421616, 69974281748, 35535207035048, 36224521019293188, 74004483908461354689, 302712665772844097945072, 2477999475270966827490305948, 40583406022745170376459610683073, 1329552679157905406495248763876363056
Offset: 0

Views

Author

Andrew Howroyd, Mar 16 2023

Keywords

Crossrefs

The labeled version is A011266.
Cf. A350794, A361583, A361585 (without single vertex components).

Programs

Formula

a(n) >= A361583(n).
Previous Showing 11-20 of 23 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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