login
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.
2
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, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 20, 39, 72, 128, 198, 280, 353, 399, 399, 353, 280, 198, 128, 72, 39, 20, 10, 4, 2, 1, 1, 1, 1, 2, 4, 10, 20, 50, 99, 227, 458, 934, 1711
OFFSET
0,6
COMMENTS
The colors may be interchanged.
REFERENCES
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
LINKS
F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning, B 5 (1978), 31-43.
F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning B: Urban Analytics and City Science, 5 (1978), 31-43. [Annotated scanned copy]
EXAMPLE
Triangles A106498 and A123547 begin:
n = 0
k = 0 : 1, 1
Total = 1, 1
n = 1
k = 0 : 1, 0
k = 1 : 1, 1
Total = 2, 1
n = 2
k = 0 : 1, 0
k = 1 : 1, 0
k = 2 : 2, 1
k = 3 : 1, 1
k = 4 : 1, 1
Totals = 6, 3
n = 3
k = 0 : 1, 0
k = 1 : 1, 0
k = 2 : 2, 0
k = 3 : 4, 1
k = 4 : 5, 2
k = 5 : 5, 4
k = 6 : 4, 3
k = 7 : 2, 2
k = 8 : 1, 1
k = 9 : 1, 1
Totals = 26, 14
CROSSREFS
Row sums give A007139. Cf. A007140, A123547.
Sequence in context: A369995 A242784 A265313 * A093466 A257463 A293483
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Nov 14 2006
STATUS
approved