OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
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 NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n + 3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4 .
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
M. B. Ahmadi and M. Sadeghimehr, Atom bond connectivity index of an infinite class NS1[n] of dendrimer nanostars, Optoelectronics and Advanced Materials, 4(7):1040-1042 July 2010.
Ali Reza Ashrafi and Parisa Nikzad, Kekulé index and bounds of energy for nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 4, No. 2, 2009, 383-388.
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 18 2018: (Start)
G.f.: 2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(126*2^n-22, n = 1 .. 40);
PROG
(PARI) a(n) = 126*2^n - 22; \\ Altug Alkan, May 13 2018
(PARI) Vec(2*x*(115 - 104*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018
(GAP) List([1..40], n->126*2^n-22); # Muniru A Asiru, May 13 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 13 2018
STATUS
approved