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

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

Offset: 1

Author

TORSTEN.SILLKE(AT)LHSYSTEMS.COM

Keywords

• nonn
• more

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

• Index entries for sequences related to graphical partitions

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