OFFSET
2,1
COMMENTS
For n>=2, a(n) is the first Zagreb index of the hexagonal network HX(n).
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 the hexagonal network HX(n) is M(HX(n); x,y) = 12*x^3*y^4 + 6*x^3*y^6 + 6*(n-3)*x^4*y^4 + 12*(n-2)*x^4*y^6 + (9*n^2-33*n+30)*x^6*y^6.
3*a(n) + 19 is a square. - Bruno Berselli, May 18 2018
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
S. Hayat and M. Imran, Computation of topological indices of certain networks, Applied Mathematics and Computation, 240, 2014, 213-228/
M. N. Husin and R. Hasni, More results on computation of topological indices of certain networks, Int. J. Networking and Virtual Organisations, 17, No. 1, 2017, 46-63.
B. Rajan, A. William, C. Grigorius, and S. Stephen, On certain topological indices of silicate, honeycomb and hexagonal networks, J. Comp. & Math. Sci., 3, No. 5, 2012, 530-535.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, May 18 2018: (Start)
G.f.: 6*x^2*(15 + 22*x - x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
(End)
MAPLE
seq(114-228*n+108*n^2, n = 2 .. 40);
PROG
(GAP) List([2..40], n->108*n^2-228*n+114); # Muniru A Asiru, May 18 2018
(PARI) a(n) = 108*n^2 - 228*n + 114; \\ Altug Alkan, May 18 2018
(PARI) Vec(6*x^2*(15 + 22*x - x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, May 18 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 17 2018
STATUS
approved