A327372 Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).

1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 3, 1, 1, 1, 1, 11, 5, 4, 1, 2, 0, 62, 29, 18, 6, 4, 2, 1, 510, 225, 101, 32, 13, 4, 3, 0, 7459, 2674, 842, 223, 72, 19, 9, 3, 1, 197867, 50834, 10784, 2171, 504, 115, 34, 9, 4, 0, 9808968, 1653859, 228863, 32322, 5268, 944, 209, 46, 16, 4, 1

Offset

0,11

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

Gus Wiseman, The unlabeled graphs covering 5 vertices with k endpoints.

Formula

Column-wise first differences of A327371.

Example

Triangle begins:
   1
   0  0
   0  0  1
   1  0  1  0
   3  1  1  1  1
  11  5  4  1  2  0

Prog

(PARI) \\ Needs G(n) defined in A327371.
T(n)={my(v=Vec(G(n)*(1 - x))); vector(#v, n, Vecrev(v[n], n))}
my(A=T(10)); for(n=1, #A, print(A[n])) \\ Andrew Howroyd, Jan 11 2024

Crossrefs

Row sums are A002494.

Column k = 0 is A261919.

The non-covering version is A327371.

The labeled version is A327377.

Cf. A000088, A004110, A294217, A327227, A327369, A327370.

Sequence in context: A200473 A361948 A180172 * A328323 A090751 A344759

Adjacent sequences: A327369 A327370 A327371 * A327373 A327374 A327375

Keyword

nonn,tabl

Author

Gus Wiseman, Sep 04 2019

Extensions

Terms a(21) and beyond from Andrew Howroyd, Sep 11 2019

Status

approved