A384843 Wiener index of the n-Dorogovtsev-Goltsev-Mendes graph.

1, 3, 21, 204, 2130, 22245, 229119, 2325966, 23319708, 231384327, 2276119977, 22228324368, 215745006246, 2082918495849, 20017195390995, 191593142789010, 1827283815276144, 17372064324294411, 164687169445632573, 1557231841690641492, 14690512431146615802

Offset: 0

Author

Andrew Howroyd, Jun 10 2025

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Eric Weisstein's World of Mathematics, Dorogovtsev-Goltsev-Mendes Graph.
• Eric Weisstein's World of Mathematics, Wiener Index.
• Index entries for linear recurrences with constant coefficients, signature (22,-156,378,-243).

Crossrefs

Cf. A384844.

Programs

Mathematica

A384843[n_] := If[n == 0, 1, 3*(1 + 10*3^(n - 2) + 3*(4*n + 7)*9^(n - 2))/8];
Array[A384843, 25, 0] (* Paolo Xausa, Jun 18 2025 *)

PARI

a(n) = if(n == 0, 1, 3*(1 + 10*3^(n-2) + 3*(4*n + 7)*9^(n-2))/8)

Formula

a(n) = 3*(1 + 10*3^(n-2) + 3*(4*n + 7)*9^(n-2))/8 for n > 0.

a(n) = 22*a(n-1) - 156*a(n-2) + 378*a(n-3) - 243*a(n-4) for n > 4.

a(n) = Sum_{k=1..n} k*A384844(n,k) for n > 0.

G.f.: 1 + 3*x*(1 - 15*x + 70*x^2 - 72*x^3)/((1 - x)*(1 - 3*x)*(1 - 9*x)^2).

E.g.f.: (8 + 27*exp(x) + 30*exp(3*x) + exp(9*x)*(7 + 36*x))/72. - Stefano Spezia, Jun 14 2025