cp's OEIS Frontend

A277107 a(n) = 16*3^n - 48.

%I A277107 #34 Jun 17 2025 22:22:35
%S A277107 0,96,384,1248,3840,11616,34944,104928,314880,944736,2834304,8503008,
%T A277107 25509120,76527456,229582464,688747488,2066242560,6198727776,
%U A277107 18596183424,55788550368,167365651200,502096953696,1506290861184,4518872583648,13556617751040
%N A277107 a(n) = 16*3^n - 48.
%C A277107 a(n) is the second Zagreb index of the Sierpiński [Sierpinski] gasket graph S[n] (n>=2).
%C A277107 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 A277107 The M-polynomial of the Sierpinski gasket graph S[n] is  M(S[n], x, y) = 6*x^2*y^4 + (3^n - 6)*x^4*y^4.
%H A277107 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 A277107 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpiński Gasket Graph</a>.
%H A277107 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A277107 G.f.: 96*x^2/((1 - x)*(1 - 3*x)).
%F A277107 a(n) = 4*a(n-1) - 3*a(n-2).
%F A277107 a(n) = 96*A003462(n-1). - _R. J. Mathar_, Apr 07 2022
%p A277107 seq(16*3^n-48, n = 1..30);
%t A277107 Table[16*3^n - 48, {n, 25}] (* or *) Rest@ CoefficientList[Series[96 x^2/((1 - x) (1 - 3 x)), {x, 0, 25}], x] (* _Michael De Vlieger_, Nov 06 2016 *)
%t A277107 LinearRecurrence[{4,-3},{0,96},30] (* _Harvey P. Dale_, Dec 20 2024 *)
%Y A277107 Cf. A277106.
%K A277107 nonn,easy
%O A277107 1,2
%A A277107 _Emeric Deutsch_, Nov 05 2016