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Number of even graphical partitions of order 2n - number of odd graphical partitions of order 2n.
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%I #10 Jan 11 2024 10:58:40

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

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

%C 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

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

%H <a href="/index/Gra#graph_part">Index entries for sequences related to graphical partitions</a>

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

%F a(n) = A029891(2*n) - A029890(2*n). - _Andrew Howroyd_, Jan 10 2024

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

%K nonn,more

%O 1,2

%A TORSTEN.SILLKE(AT)LHSYSTEMS.COM