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.

Showing 1-10 of 10 results.

A035512 Number of unlabeled strongly connected digraphs with n nodes.

Original entry on oeis.org

1, 1, 1, 5, 83, 5048, 1047008, 705422362, 1580348371788, 12139024825260556, 328160951349343885604, 31831080872412589394328804, 11234274997368899732057135454531, 14576252633139820879894296847900227082
Offset: 0

Views

Author

Ronald C. Read

Keywords

References

  • F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 218.
  • V. A. Liskovets, A contribution to the enumeration of strongly connected digraphs, Dokl. AN BSSR, 17 (1973), 1077-1080, MR49#4849.
  • R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
  • R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

Links

Crossrefs

The labeled version is A003030.
Row sums of A057276.
Column sums of A350753.
Cf. A003085, A049387, A350489, A350752.

Programs

Extensions

a(12) and a(13) added by N. J. A. Sloane from the Robinson report, Oct 17 2006

A057276 Triangle T(n,k) of number of strongly connected digraphs on n unlabeled nodes and with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 4, 16, 22, 22, 11, 5, 1, 1, 0, 0, 0, 0, 0, 1, 7, 58, 240, 565, 928, 1065, 953, 640, 359, 150, 59, 16, 5, 1, 1, 0, 0, 0, 0, 0, 0, 1, 10, 165, 1281, 6063, 19591, 47049, 87690, 131927, 163632, 170720, 151238, 115122, 75357, 42745, 20891, 8877, 3224, 1039, 286, 76, 17, 5, 1, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

Examples

			Triangle begins:
  [1] 1;
  [2] 0,0,1;
  [3] 0,0,0,1,2,1,1;
  [4] 0,0,0,0,1,4,16,22,22,11,5,1,1;
  ...
The number of strongly connected digraphs on 3 unlabeled nodes is 5 = 1+2+1+1.

Links

Crossrefs

Row sums give A035512.
Column sums give A350752.
The labeled version is A057273.
Cf. A054733, A057270, A057277, A057278, A057279, A350489.

Programs

Extensions

Terms a(46) and beyond from Andrew Howroyd, Jan 13 2022

A053454 Number of weakly connected digraphs with n arcs.

Original entry on oeis.org

1, 1, 4, 12, 53, 237, 1306, 7537, 47913, 322253, 2297874, 17191216, 134505656, 1095715055, 9267223594, 81162609328, 734511656413, 6856030049629, 65899370570285, 651338242941020, 6611459646337423, 68842439737228261
Offset: 0

Views

Author

Vladeta Jovovic, Jan 12 2000

Keywords

Links

Crossrefs

Column sums of A054733.
Row sums of A350789.
Cf. A003085, A053418, A350752.

Programs

  • PARI
    \\ See A054733 for G, InvEulerMTS.
seq(n)=Vec(subst(Pol(InvEulerMTS(sum(i=0, n, G(i, y+O(y^n))*x^i, O(x*x^n)))), x, 1)) \\ Andrew Howroyd, Jan 28 2022

Formula

Inverse Euler transform of A053418. - Max Alekseyev, Jan 22 2010

Extensions

Extended by Max Alekseyev, Jan 22 2010
a(0)=1 prepended by Andrew Howroyd, Jan 28 2022

A350796 Number of unlabeled digraphs with n arcs and a global source and sink.

Original entry on oeis.org

1, 1, 1, 2, 7, 25, 108, 513, 2690, 15230, 92361, 594669, 4040283, 28817783, 214898429, 1669663193, 13476692136, 112722792293, 974931812942, 8702563358405, 80039193725904, 757342429877879, 7362651015248190, 73451961108974776, 751144076656119144, 7866092802569673370
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A350795.
Cf. A350752, A350794, A350798, A350906, A350907.

Programs

A350798 Number of unlabeled digraphs with n arcs and a global source (or sink).

Original entry on oeis.org

1, 1, 2, 6, 21, 84, 387, 1953, 10802, 64267, 408489, 2750686, 19518841, 145236878, 1128884559, 9135566309, 76758391212, 667993213393, 6008434514996, 55755719348210, 532896254763646, 5238211003916685, 52885470406233727, 547751388283907208, 5813693205313803535, 63170000832869927871
Offset: 0

Views

Author

Andrew Howroyd, Jan 21 2022

Keywords

Crossrefs

Column sums of A350797.
Cf. A350360, A350752, A350796, A350906, A350907.

Programs

A139627 Number of strongly connected directed multigraphs with loops allowed and with n arcs.

Original entry on oeis.org

1, 1, 2, 4, 12, 37, 162, 738, 3928, 22436, 138716, 911529, 6339770, 46336941, 354453138, 2826472249, 23423053967, 201179882629, 1786791372857, 16377359709120, 154644691266520, 1502016160624186, 14985219655673207, 153377735526218010, 1608741204839374373
Offset: 0

Views

Author

Benoit Jubin, May 01 2008

Keywords

Comments

The term a(0)=1 can be interpreted as either a singleton vertex or the graph with no vertices. - Andrew Howroyd, Jan 14 2022

Links

Crossrefs

Row sums of A139622.
Cf. A052171, A350489, A350752.

Programs

Extensions

3 more terms from R. J. Mathar, Aug 04 2017
Terms a(7) and beyond from Andrew Howroyd, Jan 14 2022

A350753 Triangle read by rows: T(n,k) is the number of unlabeled strongly connected digraphs with n arcs and k vertices, n >= 0, k = 1..n+1.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 4, 1, 0, 0, 0, 1, 16, 7, 1, 0, 0, 0, 0, 22, 58, 10, 1, 0, 0, 0, 0, 22, 240, 165, 14, 1, 0, 0, 0, 0, 11, 565, 1281, 365, 18, 1, 0, 0, 0, 0, 5, 928, 6063, 4838, 733, 23, 1, 0, 0, 0, 0, 1, 1065, 19591, 38516, 14661, 1317, 28, 1, 0
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2022

Keywords

Examples

			Triangle begins:
  1;
  0, 0;
  0, 1, 0;
  0, 0, 1,  0;
  0, 0, 2,  1,   0;
  0, 0, 1,  4,   1,    0;
  0, 0, 1, 16,   7,    1,   0;
  0, 0, 0, 22,  58,   10,   1,  0;
  0, 0, 0, 22, 240,  165,  14,  1, 0;
  0, 0, 0, 11, 565, 1281, 365, 18, 1, 0;

Crossrefs

Row sums are A350752.
Column sums are A035512.
Cf. A057276 (transpose), A350450, A350489.

Programs

  • PARI
    \\ See PARI link in A350489 for program code.
my(A=A350753rows(10)); for(n=1, #A, print(A[n]))

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

A350751 Number of unlabeled strongly connected oriented graphs with n arcs.

Original entry on oeis.org

1, 0, 0, 1, 1, 3, 7, 27, 120, 590, 3172, 18291, 112597, 731646, 5002261, 35805035, 267427870, 2077890719, 16753007782, 139843832074, 1206213748404, 10731971520412, 98340872850392, 926788397662602, 8971598464914888, 89105060389927172, 907030917078092542
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2022

Keywords

Crossrefs

Column sums of A350750.
Cf. A350489, A350752.

Programs

Showing 1-10 of 10 results.

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

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