A332760 Triangle of number of connected graphs with n>=2 nodes and maximum degree 1<=k<n.

1, 0, 2, 0, 2, 4, 0, 2, 8, 11, 0, 2, 27, 49, 34, 0, 2, 62, 289, 344, 156, 0, 2, 192, 1735, 4457, 3687, 1044, 0, 2, 529, 11676, 63493, 109623, 63411, 12346, 0, 2, 1731, 87669, 1067440, 3835541, 4540334, 1909186, 274668, 0, 2

Offset

2,3

Links

Table of n, a(n) for n=2..48.

Mathoverflow, What is the number of connected graphs with n vertices of max. degree up to D?

Formula

T(n,n-1) = A000088(n-1).

T(n,2) = 2 for n>2 as the only possibilities are a cycle graph or a path graph.

Example

Triangle starts
1;
0,  2;
0,  2,  4;
0,  2,  8,    11;
0,  2,  27,   49,   34;
0,  2,  62,  289,  344,  156;
0,  2, 192, 1735, 4457, 3687, 1044;
0,  2,...

Crossrefs

Cf. A263293, A001349 (row sums), A000088.

Sequence in context: A061930 A209691 A221683 * A199335 A141660 A368500

Adjacent sequences: A332757 A332758 A332759 * A332761 A332762 A332763

Keyword

nonn,tabl,more

Author

Henry Bottomley, Feb 22 2020

Extensions

a(32)-a(48) from Chai Wah Wu, Sep 08 2020

Status

approved