OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the nanostar dendrimer D[n] from the Ghorbani et al. reference.
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 D[n] is M(D[n]; x,y) = 12*(2^n - 1)*x^2*y^2 + 3*(5*2^n - 8)*x^2*y^3 + 3*(2*2^n - 3)*x^3*y^3.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 15 2018: (Start)
G.f.: 6*x*(16 + 21*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(159*2^n-222, n = 1 .. 40);
MATHEMATICA
Rest@ CoefficientList[Series[6 x (16 + 21 x)/((1 - x) (1 - 2 x)), {x, 0, 38}], x] (* or *)
LinearRecurrence[{3, -2}, {96, 414}, 38] (* or *)
Array[159*2^# - 222 &, 38] (* Michael De Vlieger, May 15 2018 *)
PROG
(GAP) List([1..40], n->159*2^n-222); # Muniru A Asiru, May 15 2018
(PARI) Vec(6*x*(16 + 21*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 15 2018
STATUS
approved