OFFSET
1,1
COMMENTS
a(n) = the second Zagreb index of the dendrimer nanostar NS2[n], defined pictorially in Fig. 2 of the Madanshekaf reference.
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of NS2[n] is M(NS2[n]; x,y) = 3*2^n*x*y^2 + (27*2^n - 24)*x^2*y^2 + (33*2^n - 18)*x^2*y^3 + 6*2^n*x^3*y^3.
REFERENCES
A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, No. 5-6, 2011, 1075-1080.
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.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 15 2018: (Start)
G.f.: 12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(366*2^n-204, n = 1 .. 40);
MATHEMATICA
Array[366*2^# - 204 &, 29] (* Michael De Vlieger, May 14 2018 *)
PROG
(GAP) List([1..40], n->366*2^n-204); # Muniru A Asiru, May 15 2018
(PARI) Vec(12*x*(44 - 27*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 14 2018
STATUS
approved