A358243 - OEIS

A358243

Number of n-regular, N_0-weighted pseudographs on 2 vertices with total edge weight 3, up to isomorphism.

1, 4, 9, 15, 21, 28, 34, 41, 47, 54, 60, 67, 73, 80, 86, 93, 99, 106, 112, 119, 125, 132, 138, 145, 151, 158, 164, 171, 177, 184, 190, 197, 203, 210, 216, 223, 229, 236, 242, 249, 255, 262, 268, 275, 281, 288, 294, 301, 307, 314, 320, 327, 333, 340, 346, 353

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Pseudographs are finite graphs with undirected edges without identity, where parallel edges between the same vertices and loops are allowed.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

Apparently a(n) = A258589(n-2) + 2 for n>= 4, i.e., terms satisfy linear recurrence a(n) = a(n-1) + a(n-2) - a(n-3) for n>=7. - Hugo Pfoertner, Dec 02 2022

From Andrew Howroyd, Nov 23 2025: (Start)

The above observation is correct. See A390167 for an explanation.

a(n) = (26*n + (-1)^n - 45)/4 for n >= 4.

G.f.: x*(1 + 3*x + 4*x^2 + 3*x^3 + x^4 + x^5)/((1 - x)^2*(1 + x)). (End)

MATHEMATICA

LinearRecurrence[{1, 1, -1}, {1, 4, 9, 15, 21, 28}, 60] (* Paolo Xausa, May 17 2026 *)

PROG

(PARI) Vec((1 + 3*x + 4*x^2 + 3*x^3 + x^4 + x^5)/((1 - x)^2*(1 + x)) + O(x^60)) \\ Andrew Howroyd, Nov 23 2025

CROSSREFS

Row n=3 of A390167.

Other total edge weights 4 (A358244), 5 (A358245), 6 (A358246), 7 (A358247), 8 (A358248), 9 (A358249).

Cf. A258589.