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URL: https://oeis.org/A390166

⇱ A390166 - OEIS

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A390166
Number of edge-weighted n-regular multigraphs on 2 unlabeled vertices with total edge weight n.
2
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 22 2025
STATUS
approved