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%I #16 Sep 08 2022 08:46:21
%S 24,188,516,1172,2484,5108,10356,20852,41844,83828,167796,335732,
%T 671604,1343348,2686836,5373812,10747764,21495668,42991476,85983092,
%U 171966324,343932788,687865716,1375731572,2751463284,5502926708,11005853556,22011707252,44023414644,88046829428,176093658996,352187318132
%N a(n) = 164*2^n - 140.
%C a(n) is the second Zagreb index of the second type dendrimer nanostar NS2[n], defined pictorially in the Chen et al. reference (Fig. 1).
%C The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
%C The M-polynomial of NS2[n] is M(NS2[n]; x, y) = 2*(4*2^n-1)*x^2*y^2 + 16*(2*n - 1)*x^2*y^3 + 4*(2^n - 1)*x^3*y^3 (n>=0).
%H S. Chen and J. Yang, <a href="http://www.m-hikari.com/imf-2011/5-8-2011/chenshuboIMF5-8-2011.pdf">Second-order and third-order connectivity indices of dendrimer nanostars</a>, International Mathematical Forum, 6, No, 5, 2011, 223-228.
%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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F From _Vincenzo Librandi_, May 28 2018: (Start)
%F G.f.: 4*(6 + 29*x)/((1 - 2*x)*(1 - x)).
%F a(n) = 3*a(n-1) - 2*a(n-2). (End)
%p seq(164*2^n-140, n = 0 .. 40);
%t Table[164 2^n - 140, {n, 0, 33}] (* _Vincenzo Librandi_, May 28 2018 *)
%o (Magma) [164*2^n-140: n in [0..33]]; // _Vincenzo Librandi_, May 28 2018
%Y Cf. A305163, A305164, A305165.
%K nonn,easy
%O 0,1
%A _Emeric Deutsch_, May 27 2018
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