A123547 -id:A123547 - cp's OEIS frontend

A007140 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.

1, 1, 3, 14, 115, 2086, 101791, 14835870, 6852422567, 10338780759514, 51804974736769271, 872530598196790164797, 49930445153769776449253479, 9805619466642079028742952893709, 6670375074613812276139335045628924297, 15853216549413764390038207575938343994222273

Offset: 0

N. J. A. Sloane

nonn

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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]

Row sums of A123547.

Cf. A007139, A054976, A319155.

a(n) = (A054976(n) + A319155(n)) / 2. - Andrew Howroyd, Sep 25 2018

a(11)-a(15) from Andrew Howroyd, Sep 25 2018

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.

Original entry on oeis.org

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

N. J. A. Sloane, Nov 14 2006

The colors may be interchanged.

			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

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

R. W. Robinson, Rows 0 through 7, flattened
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]

Row sums give A007139. Cf. A007140, A123547.

cp's OEIS Frontend

A007140 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.

Views

Author

Keywords

References

Links

Crossrefs

Formula

Extensions