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.

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, 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, 24, 328, 2001, 3835, 2001, 328, 24, 1, 0, 0, 1, 29, 565, 5745, 20755, 20755

Offset

0,13

References

J. G. Lee, Almost Distributive Lattice Varieties, Algebra Universalis, 21 (1985), 280-304.

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

Links

R. W. Robinson, First 20 rows, 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. See Table 2.

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] See Table 2.

Example

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.
0 0 1
Total( 0)= 1
0 1 0
1 0 0
Total( 1)= 0
0 2 0
1 1 1
2 0 0
Total( 2)= 1
0 3 0
1 2 1
2 1 1
3 0 0
Total( 3)= 2
0 4 0
1 3 1
2 2 3
3 1 1
4 0 0
Total( 4)= 5
0 5 0
1 4 1
2 3 5
3 2 5
4 1 1
5 0 0
Total( 5)= 12
0 6 0
1 5 1
2 4 8
3 3 17
4 2 8
5 1 1
6 0 0
Total( 6)= 35

Crossrefs

Row sums give A055192. See A056152 for a version of this triangle with the bounding zeros in each row.

Sequence in context: A330248 A247505 A117389 * A098158 A110319 A036872

Adjacent sequences: A122080 A122081 A122082 * A122084 A122085 A122086

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 19 2006

Status

approved