OFFSET
0,1
COMMENTS
a(n) (n>=0) is the first Zagreb index of the nanostar dendrimer G(n), defined pictorially in the Darafsheh et al. reference (see Fig. 1, where G(2) is shown).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of G(n) is M(G(n); x, y) = 8*2^n*x^2*y^2 + (16*2^n - 12)*x^2*y^3 + (4*2^n - 3)*x^3*y^3
REFERENCES
M. R. Darafsheh, M. H. Khalifeh, Calculation of the Wiener, Szeged, and PI indices of a certain nanostar dendrimer, Ars Comb., 100, 2011, 289-298.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 29 2018: (Start)
G.f.: 2*(29 + 10*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
MAPLE
seq(136*2^n-78, n = 0 .. 40);
PROG
(PARI) Vec(2*(29 + 10*x) / ((1 - x)*(1 - 2*x)) + O(x^50)) \\ Colin Barker, May 29 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 28 2018
STATUS
approved