A278123 - OEIS

%I #15 Sep 08 2022 08:46:17

%S 194,688,1676,3652,7604,15508,31316,62932,126164,252628,505556,

%T 1011412,2023124,4046548,8093396,16187092,32374484,64749268,129498836,

%U 258997972,517996244,1035992788,2071985876,4143972052,8287944404,16575889108,33151778516,66303557332

%N a(n) = 247*2^n - 300.

%C a(n) is the second Zagreb index of the nanostar dendrimer NSC5C6[n].

%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. 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 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.: 2*x*(97 + 53*x)/((1 - x)*(1 - 2*x)).

%p seq(247*2^n-300, n = 1..35);

%o (Magma) [247*2^n-300: n in [1..30]]; // _Vincenzo Librandi_, Nov 13 2016

%Y Cf. A278122.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Nov 12 2016