OFFSET
0,1
COMMENTS
a(n) is the first Zagreb index of the micelle-like chiral dendrimer B[n]. 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 B[n] can be viewed in the Yousefi-Azari et al. references.
The M-polynomial of the micelle-like chiral dendrimer B[n] is M(B[n],x,y) = (8*2^n + 2)*x*y^2 + 12*x^2*y^2 + (56*2^n - 10)*x^2*y^3 + (8*2^n +5)*x^3*y^3.
LINKS
Emeric Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
H. Yousefi-Azari, A. R. Ashrafi, and M. H. Khalifeh, Wiener index of micelle-like chiral dendrimers, Studia UBB, Chemia, 55, No. 4, 125-130, 2010.
H. Yousefi-Azari and A. R. Ashrafi, Computing PI index of micelle-like chiral dendrimers, Bulgarian Chem. Commun., 44, 4, 2012, 307-309.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
G.f.: 2*(193 - 210*x)/((1-x)*(1-2*x)).
MAPLE
seq(352*2^n+34, n = 0..35);
MATHEMATICA
352*2^Range[0, 30]+34 (* or *) LinearRecurrence[{3, -2}, {386, 738}, 30] (* Harvey P. Dale, Jul 12 2021 *)
PROG
(Magma) [352*2^n+34: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 12 2016
STATUS
approved