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A106498 Triangle read by rows: T(n,k) = number of unlabeled bicolored graphs with isolated nodes allowed having 2n nodes and k edges, with n nodes of each color. Here n >= 0, 0 <= k <= n^2.

%I A106498 #12 Jun 22 2017 10:23:17
%S A106498 1,1,1,1,1,2,1,1,1,1,2,4,5,5,4,2,1,1,1,1,2,4,10,13,23,26,32,26,23,13,
%T A106498 10,4,2,1,1,1,1,2,4,10,20,39,72,128,198,280,353,399,399,353,280,198,
%U A106498 128,72,39,20,10,4,2,1,1,1,1,2,4,10,20,50,99,227,458,934,1711
%N A106498 Triangle read by rows: T(n,k) = number of unlabeled bicolored graphs with isolated nodes allowed having 2n nodes and k edges, with n nodes of each color. Here n >= 0, 0 <= k <= n^2.
%C A106498 The colors may be interchanged.
%D A106498 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H A106498 R. W. Robinson, <a href="/A106498/b106498.txt">Rows 0 through 7, flattened</a>
%H A106498 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 A106498 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]
%e A106498 Triangles A106498 and A123547 begin:
%e A106498 n = 0
%e A106498 k = 0 : 1, 1
%e A106498 Total = 1, 1
%e A106498 n = 1
%e A106498 k = 0 : 1, 0
%e A106498 k = 1 : 1, 1
%e A106498 Total = 2, 1
%e A106498 n = 2
%e A106498 k = 0 : 1, 0
%e A106498 k = 1 : 1, 0
%e A106498 k = 2 : 2, 1
%e A106498 k = 3 : 1, 1
%e A106498 k = 4 : 1, 1
%e A106498 Totals = 6, 3
%e A106498 n = 3
%e A106498 k = 0 : 1, 0
%e A106498 k = 1 : 1, 0
%e A106498 k = 2 : 2, 0
%e A106498 k = 3 : 4, 1
%e A106498 k = 4 : 5, 2
%e A106498 k = 5 : 5, 4
%e A106498 k = 6 : 4, 3
%e A106498 k = 7 : 2, 2
%e A106498 k = 8 : 1, 1
%e A106498 k = 9 : 1, 1
%e A106498 Totals = 26, 14
%Y A106498 Row sums give A007139. Cf. A007140, A123547.
%K A106498 nonn,tabf
%O A106498 0,6
%A A106498 _N. J. A. Sloane_, Nov 14 2006