|
%I #22 Sep 08 2022 08:46:17
%S 160,568,1384,3016,6280,12808,25864,51976,104200,208648,417544,835336,
%T 1670920,3342088,6684424,13369096,26738440,53477128,106954504,
%U 213909256,427818760,855637768,1711275784,3422551816,6845103880,13690208008,27380416264,54760832776
%N a(n) = 204*2^n - 248.
%C a(n) is the first Zagreb index of the nanostar dendrimer NSC5C6[n].
%C 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. The pictorial definition of NSC5C6[n] can be viewed in the A. R. Ashrafi et al. and in the M. Rostami et al. references.
%C The M-polynomial of the nanostar dendrimer NSC5C6[n] is M(NSC5C6[n],x,y) = (4*2^n - 6)*x*y^3 + 4*2^n*x*y^4 + (4*2^n -6)*x^2*y^2 + (18*2^n - 28)*x^2*y^3 + 2*2^n*x^2*y^4 + (7*2^n - 10)*x^3*y^3 + 2^n*x^4*y^4.
%H A. R. Ashrafi and P. Nikzad, <a href="http://www.chalcogen.ro/1Ashrafi-Nikzad.pdf">Szeged index of nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 4, No. 1, 2009, 155-157.
%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 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 M. Rostami, M. Shabanian, and H. Moghanian, <a href="http://www.chalcogen.ro/247_Rostami.pdf">Some topological indices for theoretical study of two types of nanostar dendrimers</a>, Digest J. of Nanomaterials and Biostructures, 7, 1, 2012, 247-252.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F G.f.: 8*x*(20 + 11*x)/((1 - x)*(1 - 2*x)).
%p seq(204*2^n-248, n = 1..35);
%o (Magma) [204*2^n-248: n in [1..35]]; // _Vincenzo Librandi_, Nov 13 2016
%o (PARI) a(n)=204*2^n-248 \\ _Charles R Greathouse IV_, Nov 13 2016
%Y Cf. A278123.
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Nov 12 2016
|
