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Number of unlabeled bicolored graphs, with no isolated nodes, on 2n nodes having n nodes of each color and allowing the color classes to be interchanged.
(Formerly M2980)
5

%I M2980 #23 Sep 25 2018 18:44:30

%S 1,1,3,14,115,2086,101791,14835870,6852422567,10338780759514,

%T 51804974736769271,872530598196790164797,49930445153769776449253479,

%U 9805619466642079028742952893709,6670375074613812276139335045628924297,15853216549413764390038207575938343994222273

%N Number of unlabeled bicolored graphs, with no isolated nodes, on 2n nodes having n nodes of each color and allowing the color classes to be interchanged.

%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H F. Harary, L. March and R. W. Robinson, <a href="https://doi.org/10.1068/b050031">On enumerating certain design problems in terms of bicolored graphs with no isolates</a>, Environment and Planning, B 5 (1978), 31-43.

%H F. Harary, L. March and R. W. Robinson, <a href="/A007139/a007139.pdf">On enumerating certain design problems in terms of bicolored graphs with no isolates</a>, Environment and Planning B: Urban Analytics and City Science, 5 (1978), 31-43. [Annotated scanned copy]

%F a(n) = (A054976(n) + A319155(n)) / 2. - _Andrew Howroyd_, Sep 25 2018

%Y Row sums of A123547.

%Y Cf. A007139, A054976, A319155.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E a(11)-a(15) from _Andrew Howroyd_, Sep 25 2018