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A122083 Triangle read by rows in which row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color, with no isolated nodes; the color classes are not interchangeable.

%I A122083 #6 Jun 22 2017 10:45:23
%S A122083 1,0,0,0,1,0,0,1,1,0,0,1,3,1,0,0,1,5,5,1,0,0,1,8,17,8,1,0,0,1,11,42,
%T A122083 42,11,1,0,0,1,15,91,179,91,15,1,0,0,1,19,180,633,633,180,19,1,0,0,1,
%U A122083 24,328,2001,3835,2001,328,24,1,0,0,1,29,565,5745,20755,20755
%N A122083 Triangle read by rows in which row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color, with no isolated nodes; the color classes are not interchangeable.
%D A122083 J. G. Lee, Almost Distributive Lattice Varieties, Algebra Universalis, 21 (1985), 280-304.
%D A122083 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%H A122083 R. W. Robinson, <a href="/A122083/b122083.txt">First 20 rows, flattened</a>
%H A122083 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. See Table 2.
%H A122083 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] See Table 2.
%e A122083 K M N Gives the number N of unlabeled bicolored graphs with no isolated nodes and having K nodes of one color and M nodes of the other color.
%e A122083 0 0 1
%e A122083 Total( 0)= 1
%e A122083 0 1 0
%e A122083 1 0 0
%e A122083 Total( 1)= 0
%e A122083 0 2 0
%e A122083 1 1 1
%e A122083 2 0 0
%e A122083 Total( 2)= 1
%e A122083 0 3 0
%e A122083 1 2 1
%e A122083 2 1 1
%e A122083 3 0 0
%e A122083 Total( 3)= 2
%e A122083 0 4 0
%e A122083 1 3 1
%e A122083 2 2 3
%e A122083 3 1 1
%e A122083 4 0 0
%e A122083 Total( 4)= 5
%e A122083 0 5 0
%e A122083 1 4 1
%e A122083 2 3 5
%e A122083 3 2 5
%e A122083 4 1 1
%e A122083 5 0 0
%e A122083 Total( 5)= 12
%e A122083 0 6 0
%e A122083 1 5 1
%e A122083 2 4 8
%e A122083 3 3 17
%e A122083 4 2 8
%e A122083 5 1 1
%e A122083 6 0 0
%e A122083 Total( 6)= 35
%Y A122083 Row sums give A055192. See A056152 for a version of this triangle with the bounding zeros in each row.
%K A122083 nonn,tabl
%O A122083 0,13
%A A122083 _N. J. A. Sloane_, Oct 19 2006