cp's OEIS Frontend

A277105 a(n) = (27*3^n - 63)/2.

%I A277105 #30 Feb 16 2025 08:33:36
%S A277105 9,90,333,1062,3249,9810,29493,88542,265689,797130,2391453,7174422,
%T A277105 21523329,64570050,193710213,581130702,1743392169,5230176570,
%U A277105 15690529773,47071589382,141214768209,423644304690,1270932914133,3812798742462,11438396227449,34315188682410,102945566047293,308836698141942,926510094425889
%N A277105 a(n) = (27*3^n - 63)/2.
%C A277105 a(n) is the second Zagreb index of the Hanoi graph H[n] (n>=2).
%C A277105 The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
%C A277105 The M-polynomial of the Hanoi graph H[n] is  M(H[n],x,y) = 6*x^2*y^3 + (3/2)*(3^n - 5)*x^3*y^3.
%H A277105 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A277105 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a>
%H A277105 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A277105 O.g.f.: 9*x*(1 + 6*x)/((1 - x)*(1 - 3*x)).
%F A277105 E.g.f.: 9*(1 - exp(x))*(4 - 3*exp(x) - 3*exp(2*x))/2. - _Bruno Berselli_, Nov 14 2016
%F A277105 a(n) = 9*A116970(n+1).
%p A277105 seq((1/2)*(9*(3^(n+1)-7)), n = 1..30);
%t A277105 Table[(27 3^n - 63)/2, {n, 1, 30}] (* _Bruno Berselli_, Nov 14 2016 *)
%o A277105 (Magma) [(27*3^n-63)/2: n in [1..30]]; // _Bruno Berselli_, Nov 14 2016
%Y A277105 Cf. A116970, A277104.
%K A277105 nonn,easy
%O A277105 1,1
%A A277105 _Emeric Deutsch_, Nov 05 2016