A304841 - OEIS

%I #13 May 30 2026 16:40:47

%S 57,124,191,258,325,392,459,526,593,660,727,794,861,928,995,1062,1129,

%T 1196,1263,1330,1397,1464,1531,1598,1665,1732,1799,1866,1933,2000,

%U 2067,2134,2201,2268,2335,2402,2469,2536,2603,2670,2737,2804,2871,2938,3005,3072,3139,3206,3273,3340

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

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

%C 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.

%C 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.

%H G. Cash, S. Klavzar, M. Petkovsek, <a href="http://pubs.acs.org/doi/abs/10.1021/ci0100999">Three methods for calculation of the hyper-Wiener index of a molecular graph</a>, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.

%H E. Deutsch and Sandi Klavzar, <a href="https://doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1)

%F From _Michael De Vlieger_, May 24 2018: (Start)

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

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

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

%t Array[67 # - 10 &, 50] (* or *)

%t LinearRecurrence[{2, -1}, {57, 124}, 50] (* or *)

%t Rest@ CoefficientList[Series[(x (57 + 10 x))/(-1 + x)^2, {x, 0, 50}], x] (* _Michael De Vlieger_, May 24 2018 *)

%Y Cf. A304840.

%K nonn,easy,changed

%O 1,1

%A _Emeric Deutsch_, May 24 2018