A304841 a(n) = 67*n - 10 (n>=1).

57, 124, 191, 258, 325, 392, 459, 526, 593, 660, 727, 794, 861, 928, 995, 1062, 1129, 1196, 1263, 1330, 1397, 1464, 1531, 1598, 1665, 1732, 1799, 1866, 1933, 2000, 2067, 2134, 2201, 2268, 2335, 2402, 2469, 2536, 2603, 2670, 2737, 2804, 2871, 2938, 3005, 3072, 3139, 3206, 3273, 3340

Offset

1,1

Comments

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

The second Zagreb index of a simple connected graph is the sum of the degree products 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

Table of n, a(n) for n=1..50.

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 Michael De Vlieger, May 24 2018: (Start)

G.f.: (x*(57 + 10*x))/(-1 + x)^2.

a(n) = 2*a(n-1)-a(n-2). (End)

Maple

seq(67*n-10, n = 1 .. 50);

Mathematica

Array[67 # - 10 &, 50] (* or *)
LinearRecurrence[{2, -1}, {57, 124}, 50] (* or *)
Rest@ CoefficientList[Series[(x (57 + 10 x))/(-1 + x)^2, {x, 0, 50}], x] (* Michael De Vlieger, May 24 2018 *)

Crossrefs

Cf. A304840.

Sequence in context: A216895 A044244 A044625 * A240759 A154092 A118152

Adjacent sequences: A304838 A304839 A304840 * A304842 A304843 A304844

Keyword

nonn,easy

Author

Emeric Deutsch, May 24 2018

Status

approved