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

%I A384843 #19 Jun 18 2025 16:52:35
%S A384843 1,3,21,204,2130,22245,229119,2325966,23319708,231384327,2276119977,
%T A384843 22228324368,215745006246,2082918495849,20017195390995,
%U A384843 191593142789010,1827283815276144,17372064324294411,164687169445632573,1557231841690641492,14690512431146615802
%N A384843 Wiener index of the n-Dorogovtsev-Goltsev-Mendes graph.
%H A384843 Andrew Howroyd, <a href="/A384843/b384843.txt">Table of n, a(n) for n = 0..500</a>
%H A384843 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html">Dorogovtsev-Goltsev-Mendes Graph</a>.
%H A384843 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WienerIndex.html">Wiener Index</a>.
%H A384843 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-156,378,-243).
%F A384843 a(n) = 3*(1 + 10*3^(n-2) + 3*(4*n + 7)*9^(n-2))/8 for n > 0.
%F A384843 a(n) = 22*a(n-1) - 156*a(n-2) + 378*a(n-3) - 243*a(n-4) for n > 4.
%F A384843 a(n) = Sum_{k=1..n} k*A384844(n,k) for n > 0.
%F A384843 G.f.: 1 + 3*x*(1 - 15*x + 70*x^2 - 72*x^3)/((1 - x)*(1 - 3*x)*(1 - 9*x)^2).
%F A384843 E.g.f.: (8 + 27*exp(x) + 30*exp(3*x) + exp(9*x)*(7 + 36*x))/72. - _Stefano Spezia_, Jun 14 2025
%t A384843 A384843[n_] := If[n == 0, 1, 3*(1 + 10*3^(n - 2) + 3*(4*n + 7)*9^(n - 2))/8];
%t A384843 Array[A384843, 25, 0] (* _Paolo Xausa_, Jun 18 2025 *)
%o A384843 (PARI) a(n) = if(n == 0, 1, 3*(1 + 10*3^(n-2) + 3*(4*n + 7)*9^(n-2))/8)
%Y A384843 Cf. A384844.
%K A384843 nonn
%O A384843 0,2
%A A384843 _Andrew Howroyd_, Jun 10 2025