A390166 Number of edge-weighted n-regular multigraphs on 2 unlabeled vertices with total edge weight n.

1, 1, 4, 9, 27, 59, 147, 309, 680, 1359, 2745, 5223, 9923, 18086, 32732, 57515, 100133, 170449, 287377, 475964, 780971, 1262965, 2024448, 3205891, 5035293, 7826984, 12074562, 18460301, 28026831, 42215156, 63178973, 93888989, 138702881, 203613174, 297270739, 431527023

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Example

The a(3) = 9 multigraphs consist of either 3 edges connecting the two vertices or one edge between the vertices and a loop at each vertex. When there are 3 edges, possible edge weights are (3,0,0), (2,1,0) or (1,1,1). Otherwise with one edge and two loops possible weights are (3,0,0), (2,1,0), (1,2,0), (1,1,1), (0,3,0), (0,2,1), where (x,y,z) means the edge has weight x and the two loops weights y and z.

Prog

(PARI) vector(36, n, T(n-1, n-1)) \\ Needs T(n, k) from A390167.

Crossrefs

Main diagonal of A390167.

Sequence in context: A114618 A067758 A357752 * A304677 A214418 A164342

Adjacent sequences: A390163 A390164 A390165 * A390167 A390168 A390169

Keyword

nonn

Author

Andrew Howroyd, Nov 22 2025

Status

approved