cp's OEIS Frontend

A277106 a(n) = 8*3^n - 12.

%I A277106 #33 Jun 17 2025 22:22:53
%S A277106 12,60,204,636,1932,5820,17484,52476,157452,472380,1417164,4251516,
%T A277106 12754572,38263740,114791244,344373756,1033121292,3099363900,
%U A277106 9298091724,27894275196,83682825612,251048476860,753145430604,2259436291836,6778308875532
%N A277106 a(n) = 8*3^n - 12.
%C A277106 a(n) is the first Zagreb index of the Sierpiński [Sierpinski] gasket graph S[n].
%C A277106 The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph.
%C A277106 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 A277106 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 A277106 I. Gutman and K. C. Das, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match50/match50_83-92.pdf">The first Zagreb index 30 years after</a>, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
%H A277106 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpiński Gasket Graph</a>.
%H A277106 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A277106 G.f.: 12*x*(1 + x)/((1 - x)*(1 - 3*x)).
%F A277106 a(n) = 4*a(n-1) - 3*a(n-2).
%F A277106 a(n)=12*A048473(n-1). - _R. J. Mathar_, Apr 07 2022
%p A277106 seq(8*3^n-12, n = 1..30);
%t A277106 Array[8*3^# - 12 &, 25] (* _Robert G. Wilson v_, Nov 05 2016 *)
%t A277106 LinearRecurrence[{4,-3},{12,60},40] (* _Harvey P. Dale_, Oct 25 2020 *)
%Y A277106 Cf. A277107.
%K A277106 nonn,easy
%O A277106 1,1
%A A277106 _Emeric Deutsch_, Nov 05 2016