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A277107 a(n) = 16*3^n - 48. 1

%I #28 Apr 07 2022 07:26:22

%S 0,96,384,1248,3840,11616,34944,104928,314880,944736,2834304,8503008,

%T 25509120,76527456,229582464,688747488,2066242560,6198727776,

%U 18596183424,55788550368,167365651200,502096953696,1506290861184,4518872583648,13556617751040

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

%C a(n) is the second Zagreb index of the Sierpiński [Sierpinski] sieve graph S[n] (n>=2).

%C 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 The M-polynomial of the Sierpinski Sieve graph S[n] is M(S[n], x, y) = 6*x^2*y^4 + (3^n - 6)*x^4*y^4.

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiSieveGraph.html">Sierpiński Sieve Graph</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F G.f.: 96*x^2/((1 - x)*(1 - 3*x)).

%F a(n) = 4*a(n-1) - 3*a(n-2).

%F a(n) = 96*A003462(n-1). - _R. J. Mathar_, Apr 07 2022

%p seq(16*3^n-48, n = 1..30);

%t 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 *)

%Y Cf. A277106.

%K nonn,easy

%O 1,2

%A _Emeric Deutsch_, Nov 05 2016

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)