OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the nanostar dendrimer G[n] from the Ashrafi 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 G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, Computing Wiener and detour indices of a new type of nanostar dendrimers, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200.
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 Michael De Vlieger, May 15 2018: (Start)
G.f.: 28*x*(23 - 28*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n > 2. (End)
MAPLE
seq(252*2^n+140, n = 1 .. 40);
MATHEMATICA
CoefficientList[Series[28*(23 - 28*x)/(1 - 3*x + 2*x^2), {x, 0, 31}], x] (* or *)
LinearRecurrence[{3, -2}, {644, 1148}, 32] (* or *)
Array[252*2^# + 140 &, 32] (* Michael De Vlieger, May 15 2018 *)
PROG
(PARI) a(n) = 252*2^n + 140; \\ Altug Alkan, May 15 2018
(PARI) Vec(28*x*(23 - 28*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 2018
(GAP) List([1..40], n->252*2^n+140); # Muniru A Asiru, May 16 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 15 2018
STATUS
approved