OFFSET
0,1
COMMENTS
For n >= 1, a(n) is the first Zagreb index of the tetrameric 1,3-adamantane TA[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph. The pictorial definition of the tetrameric 1,3-adamantane can be viewed in the G. H. Fath-Tabar et al. reference.
The M-polynomial of the tetrameric 1,3-adamantane TA[n] is M(TA[n], x, y) = 6*(n+1)*x^2*y^3 + 6*(n-1)*x^2*y^4 + (n-1)*x^4*y^4.
LINKS
Emeric Deutsch and Sandi Klavžar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
G. H. Fath-Tabar, A. Azad, and N. Elahinezhad, Some topological indices of tetrameric 1,3-adamantane, Iranian J. Math. Chemistry, 1, No. 1, 2010, 111-118.
Ivan Gutman and Kinkar C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: 2*(44*x - 7)/(1-x)^2.
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Nov 13 2016
MAPLE
seq(74*n-14, n = 0..40);
MATHEMATICA
Table[74n - 14, {n, 0, 50}] (* Harvey P. Dale, Mar 08 2020 *)
PROG
(Magma) [74*n-14: n in [0..45]]; // Vincenzo Librandi, Nov 13 2016
(Scala) (0 to 48).map(74 * _ - 14) // Alonso del Arte, Mar 11 2020
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Emeric Deutsch, Nov 12 2016
STATUS
approved