A277986 - OEIS

A277986

a(n) = 74*n - 14.

-14, 60, 134, 208, 282, 356, 430, 504, 578, 652, 726, 800, 874, 948, 1022, 1096, 1170, 1244, 1318, 1392, 1466, 1540, 1614, 1688, 1762, 1836, 1910, 1984, 2058, 2132, 2206, 2280, 2354, 2428, 2502, 2576, 2650, 2724, 2798, 2872, 2946, 3020, 3094, 3168

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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

Table of n, a(n) for n=0..43.

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