OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the oxide network OX(n), defined pictorially in the Javaid et al. reference (Fig. 3, where OX(2) is shown) or in the Liu et al. reference (Fig. 6, where OX(5) 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 OX(n) is M(OX(n); x, y) = 12*n*x^2*y^4 + 6*n*(3*n - 2)*x^4*y^4 (n>=1).
a(n) + 1 is a square. - Muniru A Asiru, May 27 2018
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..5000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
M. Javaid and C. Y. Jung, M-polynomials and topological indices of silicate and oxide networks, International J. Pure and Applied Math., 115, No. 1, 2017, 129-152.
J.-B. Liu, S. Wang, C. Wang, and S. Hayat, Further results on computation of topological indices of certain networks, IET Control Theory Appl., 11, No. 13, 2017, 2065-2071.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, May 26 2018: (Start)
G.f.: 24*x*(5 + 7*x) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)
MAPLE
seq(144*n^2 - 24*n, n = 1 .. 50);
PROG
(PARI) Vec(24*x*(5 + 7*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, May 26 2018
(GAP) List([1..50], n->144*n^2-24*n); # Muniru A Asiru, May 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 26 2018
STATUS
approved