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.

Previous Showing 11-17 of 17 results.

A007721 Number of distinct degree sequences among all connected graphs with n nodes.

Original entry on oeis.org

1, 1, 2, 6, 19, 68, 236, 863, 3137, 11636, 43306, 162728, 614142, 2330454, 8875656, 33924699, 130038017, 499753560, 1924912505, 7429159770, 28723877046, 111236422377, 431403469046, 1675316533812, 6513837677642, 25354842098354, 98794053266471, 385312558567775
Offset: 1

Views

Author

Frank Ruskey

Keywords

Comments

Sometimes called "graphical partitions", although this term is deprecated.

Links

Crossrefs

Cf. A000569, A004250, A004251, A007722, A029889; A095268 (analog for all graphs).

Extensions

a(9) corrected by Gordon Royle, Aug 30 2006
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 19 2007
Prepended missing term a(1), Travis Hoppe, Aug 04 2014
a(22)-a(28) added by Wang Kai, Feb 15 2017

A029894 Number of directed (or Gale-Ryser) graphical partitions: degree-vector pairs (in-degree, out-degree) for directed graphs (loops allowed) with n vertices; or possible ordered pair (row-sum, column-sum) vectors for a 0-1 matrix.

Original entry on oeis.org

1, 2, 7, 34, 221, 1736, 15584, 153228, 1611189, 17826202, 205282376, 2441437708, 29816628471, 372314544202, 4737438631001, 61264426341926, 803488037899349, 10668478221202710, 143203795004873285, 1940953294927992976, 26536578116407809962, 365653739580163294032
Offset: 0

Views

Author

torsten.sillke(AT)lhsystems.com

Keywords

References

  • R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

Links

Crossrefs

Main diagonal of A327913.
Cf. A000569, A004250, A004251, A029889, A318396.

Programs

Formula

Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.
a(n) = F(n, n, 0, n) where F(b, c, t, w) = Sum_{i=0..b} Sum_{j=ceiling((t+i)/w)..min(t+i, c)} F(i, j, t+i-j, w-1) for w > 0, F(b, c, 0, 0) = 1 and F(b, c, t, 0) = 0 for t > 0. - Andrew Howroyd, Nov 01 2019

Extensions

"Loops allowed" added to the definition by Brendan McKay, Oct 20 2015
a(0)=1 prepended and terms a(12) and beyond from Andrew Howroyd, Oct 31 2019

A007722 Number of graphical partitions of biconnected graphs with n nodes.

Original entry on oeis.org

1, 3, 9, 34, 125, 473, 1779, 6732, 25492, 96927, 369463, 1412700, 5415117, 20807502, 80120350, 309106496, 1194609429, 4624160156, 17925278497, 69578272204, 270401326899, 1052036082719, 4097343156323, 15973179953261, 62325892264031, 243392644741599
Offset: 3

Views

Author

Frank Ruskey

Keywords

References

  • F. Ruskey, Alley CATs in search of good homes, Congress. Numerant., 102 (1994) 97-110.

Links

Crossrefs

Cf. A000569, A004250, A004251, A007721, A029889, A095268.

Extensions

a(15)-a(28) added by Kai Wang, Feb 15 2017

A029890 Number of odd graphical partitions.

Original entry on oeis.org

1, 2, 7, 20, 70, 234, 832, 2956, 10759, 39394, 145892, 543564, 2038831, 7684116, 29092055, 110550260, 421495147, 1611662256
Offset: 1

Views

Author

TORSTEN.SILLKE(AT)LHSYSTEMS.COM

Keywords

References

  • R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

Links

Crossrefs

Cf. A000569, A004250, A004251, A029889.

Formula

Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.

A029891 Number of even graphical partitions.

Original entry on oeis.org

1, 3, 7, 23, 70, 242, 832, 2983, 10759, 39482, 145892, 543877, 2038831, 7685211, 29092055, 110554267, 421495147, 1611676767
Offset: 1

Views

Author

TORSTEN.SILLKE(AT)LHSYSTEMS.COM

Keywords

References

  • R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

Links

Crossrefs

Cf. A000569, A004250, A004251, A029889.

Formula

Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.

A029893 Number of graphical partitions with up to n parts (?).

Original entry on oeis.org

1, 2, 4, 10, 24, 68, 198, 656, 2112
Offset: 1

Views

Author

torsten.sillke(AT)lhsystems.com

Keywords

References

  • R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

Links

Crossrefs

Cf. A000569, A004250, A004251, A029889.
A possible duplicate of A028506.

Formula

Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.

A029892 Number of even graphical partitions of order 2n - number of odd graphical partitions of order 2n.

Original entry on oeis.org

1, 3, 8, 27, 88, 313, 1095, 4007, 14511
Offset: 1

Views

Author

TORSTEN.SILLKE(AT)LHSYSTEMS.COM

Keywords

Comments

The graphical partitions considered here are for graphs with 2n vertices and with half-loops allowed. Half-loops are loops which count as 1 towards the degree of the vertex. See A029889 for additional information. - Andrew Howroyd, Jan 11 2024

References

  • R. A. Brualdi, H. J. Ryser, Combinatorial Matrix Theory, Cambridge Univ. Press, 1992.

Links

Crossrefs

Cf. A000569, A004250, A004251, A029889, A029890, A029891.

Formula

Calculated using Cor. 6.3.3, Th. 6.3.6, Cor. 6.2.5 of Brualdi-Ryser.
a(n) = A029891(2*n) - A029890(2*n). - Andrew Howroyd, Jan 10 2024
Previous Showing 11-17 of 17 results.

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