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 1-4 of 4 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

A350752 Number of unlabeled strongly connected digraphs with n arcs.

Original entry on oeis.org

1, 0, 1, 1, 3, 6, 25, 91, 442, 2241, 12591, 75180, 478648, 3211245, 22635956, 166828221, 1281518573, 10229858290, 84652925554, 724601312400, 6403522811765, 58327076550161, 546764617643250, 5267719312771122, 52096218005705959, 528285485054771639
Offset: 0

Views

Author

Andrew Howroyd, Jan 13 2022

Keywords

Crossrefs

Row sums of A350753.
Column sums of A057276.
Cf. A035512, A350489, A350751.

Programs

A350789 Triangle read by rows: T(n,k) is the number of unlabeled weakly connected digraphs with n arcs and k vertices, k = 1..n+1.

Original entry on oeis.org

1, 0, 1, 0, 1, 3, 0, 0, 4, 8, 0, 0, 4, 22, 27, 0, 0, 1, 37, 108, 91, 0, 0, 1, 47, 326, 582, 350, 0, 0, 0, 38, 667, 2432, 3024, 1376, 0, 0, 0, 27, 1127, 7694, 17314, 16008, 5743, 0, 0, 0, 13, 1477, 19646, 74676, 117312, 84494, 24635
Offset: 0

Views

Author

Andrew Howroyd, Jan 28 2022

Keywords

Examples

			Triangle begins:
  1;
  0, 1;
  0, 1, 3;
  0, 0, 4,  8;
  0, 0, 4, 22,   27;
  0, 0, 1, 37,  108,   91;
  0, 0, 1, 47,  326,  582,   350;
  0, 0, 0, 38,  667, 2432,  3024,  1376;
  0, 0, 0, 27, 1127, 7694, 17314, 16008, 5743;
  ...

Links

Crossrefs

Row sums are A053454.
Column sums are A003085.
Main diagonal is A000238.
Cf. A054733 (transpose), A350450 (acyclic), A350753 (strongly connected).

Programs

  • PARI
    \\ See A054733 for G, InvEulerMTS
T(n)={my(p=InvEulerMTS(sum(i=0, n, G(i, y+O(y^n))*x^i, O(x*x^n)))); vector(n, n, Vec(O(x^n)+polcoef(p,n-1,y)/x, -n))}
{ my(A=T(10)); for(n=1, #A, print(A[n])) }

A139622 Triangle read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 6, 4, 1, 1, 10, 19, 6, 1, 1, 19, 73, 59, 9, 1, 1, 28, 208, 350, 138, 12, 1, 1, 44, 534, 1670, 1361, 301, 16, 1, 1, 60, 1215, 6476, 9724, 4364, 575, 20, 1, 1, 85, 2542, 21898, 55707, 45284, 12131, 1042, 25, 1, 1, 110, 4951, 65789, 268329, 365063, 175416, 30090, 1749, 30, 1
Offset: 1

Views

Author

Benoit Jubin, May 01 2008

Keywords

Examples

			Triangle begins:
    1
    1    1
    1    2    1
    1    6    4    1
    1   10   19    6    1
    1   19   73   59    9    1
    1   28  208  350  138   12    1
    1   44  534 1670 1361  301   16  1
    ...
T(4 edges, 2 vertices)=6: one graph 1->1, 1->1, 2->1, 1->2; one graph 1->1, 2->1, 2->1, 1->2; one graph 1->1, 1->2, 1->2, 2->1; one graph 1->1, 1->2, 2->1, 2->2; one graph 2->1, 2->1, 2->1, 1->2; one graph 1->2, 1->2, 2->1, 2->1.
T(4 edges, 3 vertices)=4: one graph 1->1, 2->1, 3->2, 1->3; one graph 2->1, 2->1, 3->2, 1->3; one graph 2->1, 3->1, 1->2, 1->3; one graph 2->1, 3->1, 1->2, 2->3.

Links

Crossrefs

Row sums are A139627.
Cf. A136564, A139621, A143841, A350489, A350753.

Programs

Formula

T(n,1) = T(n,n) = 1.
T(n,2) = A139621(n,2) - n(n+1)/2.

Extensions

More terms from R. J. Mathar, Aug 11 2017
Terms a(34) and beyond from Andrew Howroyd, Jan 14 2022
Showing 1-4 of 4 results.

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

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