OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the triangulane T[n], defined pictorially in the Khalifeh 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 the triangulane T[n] is M(T[n]; x,y) = 3*2^{n-1}*x^2*y^2 + 3*2^n*x^2*y^4 + (9*2^{n-1}-6)*x^4*y^4.
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. H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, Computing Wiener and Kirchhoff indices of a triangulane, Indian J. Chemistry, 47A, 2008, 1503-1507.
Index entries for linear recurrences with constant coefficients, signature (3,-2).
FORMULA
From Colin Barker, May 13 2018: (Start)
G.f.: 24*x*(3 - x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2. (End)
MAPLE
seq(60*2^n - 48, n=1..40);
MATHEMATICA
60*2^Range[50] - 48 (* Paolo Xausa, Feb 25 2026 *)
PROG
(PARI) Vec(24*x*(3 - x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 13 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 12 2018
STATUS
approved