%I #24 May 23 2018 10:59:39

%S 754,1330,2482,4786,9394,18610,37042,73906,147634,295090,590002,

%T 1179826,2359474,4718770,9437362,18874546,37748914,75497650,150995122,

%U 301990066,603979954,1207959730,2415919282,4831838386,9663676594,19327353010,38654705842,77309411506,154618822834,309237645490,618475290802

%N a(n) = 288*2^n + 178 (n >= 1).

%C a(n) is the second Zagreb index of the nanostar dendrimer G[n] from the Ashrafi et al. reference.

%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 G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4.

%H Colin Barker, <a href="/A304608/b304608.txt">Table of n, a(n) for n = 1..1000</a>

%H A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, <a href="http://match.pmf.kg.ac.rs/electronic_versions/Match65/n1/match65n1_193-200.pdf">Computing Wiener and detour indices of a new type of nanostar dendrimers</a>, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.

%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 _Michael De Vlieger_, May 16 2018: (Start)

%F G.f.: 2*x*(377 - 466*x)/(1 - 3*x + 2*x^2).

%F a(n) = 3*a(n - 1) - 2*a(n - 2) for n > 2. (End)

%p seq(288*2^n+178, n = 1 .. 40);

%t CoefficientList[Series[2 (377 - 466 x)/(1 - 3 x + 2 x^2), {x, 0, 30}], x] (* or *)

%t LinearRecurrence[{3, -2}, {754, 1330}, 31] (* or *)

%t Array[288*2^# + 178 &, 31] (* _Michael De Vlieger_, May 16 2018 *)

%o (PARI) a(n) = 288*2^n + 178; \\ _Altug Alkan_, May 15 2018

%o (PARI) Vec(2*x*(377 - 466*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ _Colin Barker_, May 23 2018

%o (GAP) List([1..40],n->288*2^n+178); # _Muniru A Asiru_, May 16 2018

%Y Cf. A304605, A304606, A304607.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, May 15 2018