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.

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

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]

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

Adjacent sequences: A106495 A106496 A106497 * A106499 A106500 A106501

Keyword

nonn,tabf

Author

N. J. A. Sloane, Nov 14 2006

Status

approved