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 1-3 of 3 results.

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;
  ...
		

Crossrefs

Column k=1 is A035512.
Main diagonal is A003087.
Row sums are A000273.
The labeled version is A361455.

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.

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).

A361591 Triangle read by rows: T(n,k) is the number of weakly connected simple digraphs on n labeled nodes with k strongly connected components.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 0, 18, 18, 18, 0, 1606, 1098, 684, 446, 0, 565080, 263580, 116370, 55620, 26430, 0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762, 0, 3523091615568, 680637057912, 136498491360, 34626926250, 10819771830, 3694824126, 1111506858
Offset: 0

Views

Author

Andrew Howroyd, May 04 2023

Keywords

Examples

			Triangle begins:
  1;
  0,         1;
  0,         1,         2;
  0,        18,        18,       18;
  0,      1606,      1098,      684,      446;
  0,    565080,    263580,   116370,    55620,   26430;
  0, 734774776, 225806940, 68822910, 24578010, 9729090, 3596762;
  ...
		

Crossrefs

Column k=1 is A003030.
Main diagonal is A082402.
Row sums are A003027.
The unlabeled version is A361587.

Programs

  • PARI
    \\ Uses functions defined in A361455.
    T(n)={my(e=2); [Vecrev(p) | p<-Vec(serlaplace(1 + log(U(e, 1/G(e, exp(y*log(U(e, 1/G(e, DigraphEgf(n, e))))))))))]}
    { my(A=T(6)); for(i=1, #A, print(A[i])) }
Showing 1-3 of 3 results.