A304840 a(n) = 52*n - 2 (n>=1).

50, 102, 154, 206, 258, 310, 362, 414, 466, 518, 570, 622, 674, 726, 778, 830, 882, 934, 986, 1038, 1090, 1142, 1194, 1246, 1298, 1350, 1402, 1454, 1506, 1558, 1610, 1662, 1714, 1766, 1818, 1870, 1922, 1974, 2026, 2078, 2130, 2182, 2234, 2286, 2338, 2390, 2442, 2494, 2546, 2598

Offset

1,1

Comments

a(n) is the first Zagreb index of the polyazulene A[n], shown pictorially in the Cash et al. reference (Fig. 6).

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 polyazulene A[n] is M(A[n];x,y) = (n + 5)*x^2*y^2 + (6*n - 2)*x^2*y^3 + (3*n - 2)*x^3*y^3.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

G. Cash, S. Klavzar, M. Petkovsek, Three methods for calculation of the hyper-Wiener index of a molecular graph, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

From Colin Barker, May 29 2018: (Start)

G.f.: 2*x*(25 + x) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>2.

(End)

Maple

seq(52*n-2, n = 1..50);

Mathematica

52*Range[50]-2 (* Harvey P. Dale, Jan 22 2020 *)

Prog

(PARI) Vec(2*x*(25 + x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, May 29 2018

Crossrefs

Cf. A304841.

Sequence in context: A044520 A158066 A328305 * A043220 A039397 A044000

Adjacent sequences: A304837 A304838 A304839 * A304841 A304842 A304843

Keyword

nonn,easy

Author

Emeric Deutsch, May 24 2018

Status

approved